118a Liapunov Liapis Origin Gr

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Aleksandr LyapunovAleksandr Mikhailovich Lyapunov

Born: 6 June 1857 in Yaroslavl,RussiaDied: 3 Nov 1918 in Odessa, Russia

(: ? 6 [OS 25 ] 1857 - 3 1918) , . romanized Ljapunov, Liapunov Ljapunow.Lyapunov ,

,

. Lyapunov ( ) . . , . Lyapunov : ; , , . , . : ' ; ( ); , , , . . , , . , , . ( ), , .

. , n- , n n A (Hartman-Grobman). , , , , Lyapunov . ( ), eigenspaces , , . .


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, . , , , . , . , , , . . .Let f : R R be a continuously differentiable function with a fixed point a , f (a) = a.

Consider the dynamical system obtained by iterating the function f :

The fixed point a is stable if the absolute value of the derivative of f at a is strictly lessthan 1, and unstable if it is strictly greater than 1. This is because near the point a , thefunction a has a linear approximation with slope f (a):

which means that the derivative measures the rate at which the successive iteratesapproach the fixed point a or diverge from it. If the derivative at a is exactly 1 or 1,then more information is needed in order to decide stability.

There is an analogous criterion for a continuously differentiable map f : R n R n witha fixed point a , expressed in terms of its Jacobian matrix at a , J = J a( f ). If alleigenvalues of J are real or complex numbers with absolute value strictly less than 1then a is a stable fixed point; if at least one of them has absolute value strictly greater than 1 then a is unstable. Just as for n=1, the case of all eigenvalues having absolutevalue 1 needs to be investigated further the Jacobi matrix test is inconclusive. Thesame criterion holds more generally for diffeomorphisms of a smooth manifold .

Linear autonomous systems

The stability of fixed points of a system of constant coefficient linear differential

equations of first order can be analyzed using the eigenvalues of the correspondingmatrix.

An autonomous system

x' = Ax,

where x(t ) R n and A is an nn matrix with real entries, has a constant solution

x(t ) = 0.

(In a different language, the origin 0 R n is an equilibrium point of the correspondingdynamical system.) This solution is asymptotically stable as t ("in the future") if
http://en.wikipedia.org/wiki/Continuously_differentiable_functionhttp://en.wikipedia.org/wiki/Continuously_differentiable_functionhttp://en.wikipedia.org/wiki/Absolute_valuehttp://en.wikipedia.org/wiki/Derivativehttp://en.wikipedia.org/wiki/Derivativehttp://en.wikipedia.org/wiki/Linear_approximationhttp://en.wikipedia.org/wiki/Jacobian_matrixhttp://en.wikipedia.org/wiki/Eigenvalueshttp://en.wikipedia.org/wiki/Diffeomorphismhttp://en.wikipedia.org/wiki/Diffeomorphismhttp://en.wikipedia.org/wiki/Smooth_manifoldhttp://en.wikipedia.org/wiki/Linear_differential_equationhttp://en.wikipedia.org/wiki/Linear_differential_equationhttp://en.wikipedia.org/wiki/Eigenvaluehttp://en.wikipedia.org/wiki/Autonomous_system_(mathematics)http://en.wikipedia.org/wiki/Continuously_differentiable_functionhttp://en.wikipedia.org/wiki/Absolute_valuehttp://en.wikipedia.org/wiki/Derivativehttp://en.wikipedia.org/wiki/Linear_approximationhttp://en.wikipedia.org/wiki/Jacobian_matrixhttp://en.wikipedia.org/wiki/Eigenvalueshttp://en.wikipedia.org/wiki/Diffeomorphismhttp://en.wikipedia.org/wiki/Smooth_manifoldhttp://en.wikipedia.org/wiki/Linear_differential_equationhttp://en.wikipedia.org/wiki/Linear_differential_equationhttp://en.wikipedia.org/wiki/Eigenvaluehttp://en.wikipedia.org/wiki/Autonomous_system_(mathematics)


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and only if for all eigenvalues of A, Re( ) < 0. Similarly, it is asymptotically stableas t ("in the past") if and only if for all eigenvalues of A, Re( ) > 0. If thereexists an eigenvalue of A with Re( ) > 0 then the solution is unstable for t .

Application of this result in practice, in order to decide the stability of the origin for a

linear system, is facilitated by the RouthHurwitz stability criterion . The eigenvaluesof a matrix are the roots of its characteristic polynomial . A polynomial in one variablewith real coefficients is called a Hurwitz polynomial if the real parts of all roots arestrictly negative. The RouthHurwitz theorem implies a characterization of Hurwitz

polynomials by means of an algorithm that avoids computing the roots.

Non-linear autonomous systems

Asymptotic stability of fixed points of a non-linear system can often be establishedusing the HartmanGrobman theorem .

Suppose that v is a C 1-vector field in R n which vanishes at a point p, v( p)=0. Then thecorresponding autonomous system

x' = v( x)

has a constant solution

x(t ) = p.

Let J = J p(v) be the nn Jacobian matrix of the vector field v at the point p. If alleigenvalues of J have strictly negative real part then the solution is asymptoticallystable. This condition can be tested using the RouthHurwitz criterion. In 1876Lyapunov entered the Physico-Mathematical faculty of the University of SaintPetersburg , but after one month he transferred to the Mathematics department of theuniversity.

Chebyshev Aleksandr Nikolaevich Korkin Yegor Ivanovich Zolotarev. Lyapunov ,DK Bobylev. 1880 Lyapunov . . Lyapunov 1880, Andrey Markov . Lyapunov Markov . 1884 Lyapunov . Chebyshev, , Zolotarev VASILYEVNA Kovalevskaya. 1885,

Astronomique. 1904 , [1].

1895 Lyapunov , . , Lyapunov : Aleksandr Mikhailovich Lyapunov ALEKSANDROVNA Shilipova
http://en.wikipedia.org/wiki/Real_parthttp://en.wikipedia.org/wiki/Routh%E2%80%93Hurwitz_stability_criterionhttp://en.wikipedia.org/wiki/Routh%E2%80%93Hurwitz_stability_criterionhttp://en.wikipedia.org/wiki/Characteristic_polynomialhttp://en.wikipedia.org/wiki/Hurwitz_polynomialhttp://en.wikipedia.org/wiki/Hurwitz_polynomialhttp://en.wikipedia.org/wiki/Routh%E2%80%93Hurwitz_theoremhttp://en.wikipedia.org/wiki/Hartman-Grobman_theoremhttp://en.wikipedia.org/wiki/Hartman-Grobman_theoremhttp://en.wikipedia.org/wiki/Vector_fieldhttp://en.wikipedia.org/wiki/Jacobian_matrix_and_determinanthttp://en.wikipedia.org/wiki/Saint_Petersburg_State_Universityhttp://en.wikipedia.org/wiki/Saint_Petersburg_State_Universityhttp://en.wikipedia.org/wiki/Saint_Petersburg_State_Universityhttp://en.wikipedia.org/wiki/Real_parthttp://en.wikipedia.org/wiki/Routh%E2%80%93Hurwitz_stability_criterionhttp://en.wikipedia.org/wiki/Characteristic_polynomialhttp://en.wikipedia.org/wiki/Hurwitz_polynomialhttp://en.wikipedia.org/wiki/Routh%E2%80%93Hurwitz_theoremhttp://en.wikipedia.org/wiki/Hartman-Grobman_theoremhttp://en.wikipedia.org/wiki/Vector_fieldhttp://en.wikipedia.org/wiki/Jacobian_matrix_and_determinanthttp://en.wikipedia.org/wiki/Saint_Petersburg_State_Universityhttp://en.wikipedia.org/wiki/Saint_Petersburg_State_University


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Lyapunov. Aleksandr Mikhailovich , Demidovski . ALEKSANDROVNA , , () (Boris)

, .Aleksandr Mikhailovich , RM Sechenov . Lyapunov Sechenov Rafailovna Sechenov . , , 29 . Lyapunov, ALEKSANDROVNA Nizhny Novgorod ( 1932 - 1990), 1870, Lyapunov . Markov. 1876 , Markov , . Chebyshev , , . Lyapunov 1880

. 1881: , . Chebyshev Lyapunov , : -

. , ;

Lyapunov , . 1884 . Kharkov . , 12 1892 ( ). [8], [12], [16] .

Kharkov

1902. Kharkov Kharkov , , 1891 - 1898 1899 1902. Kharkov .

[13] Pavlovskaya Lyapunov Chebyshev . Chebyshev , , Lyapunov . Thomson-Tait . . Lyapunov ,


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: - , .

Lyapunov Maclaurin Jacobi . Jacobi .

1901 Lyapunov .Grigorian [1]: -

, Lyapunov . Chebyshev , , . 1917 Lyapunov

, , . , 1918 . Rafailovna Lyapunov . 31 1918 Lyapunov Lyapunov .

Lyapunov, . , , . . , 1900 1901, .

Euler. , Accademia dei Lincei (1909) (1916). , , , Kharkov . ' . , 6 1957 Sobolev AM Lyapunov , , , , , Telemechanics . [22]. , [8] Lyapunov

. [8] : , ? ? ? Lyapunov? Lyapunov NONLINEAR . . , . 1890 - 19001890 .1890St Petersburg .1890Heawood KEMPE .


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. ( .)1891Fedorov Schnflies 230 .1892Poincar Les mthodes nouvelles de la

Mcanique Cleste ( ). , . , Delaunay, , . Lagrange Laplace.1893Pearson 18 , 18, . , - .1894

Poincar .1894Borel "Borel .1894Cartan, , Lie .1895Poincar . . .1895Cantor transfinite .1895Heinrich Weber Lehrbuch der ( ).1896 Hadamard de laValle-Poussin. , , n , n / log n.1896Cesro Lezione di Geometra intrinseca .1896Frobenius .1897Hensel p-adic .1897Burali-Forti .1897Burnside .1897Frobenius .1898Frobenius Frobenius .1898 Hadamard .1899


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Hilbert Grundlagen der Geometrie ( ), .1899Lyapunov .1900

Hilbert 23 20 . , , , , Riemann, Dirichlet" . 20, .

, Lyapunov . , [1]. , Vladimir Steklov, ' : , ,

, Dean, Levakovsky, . Dean , , . Delarue. Lyapunov . . Lyapunov . [1] 1892 Lyapunov . [2] 12 1892, Nikolai Zhukovsky VB Mlodzeevski . , , . Lyapunov Kharkiv [1]. Lyapunov 1902, , . , Chebyshev. , Lyapunov Chebyshev

1908 . , Euler: 18 19 [1]. 1917, Lyapunov . Lyapunov , . 31 1918. ,Lyapunov , . [3]Lyapunov , , , . , , . Laplace . , 1897 Dirichlet . Steklov. Lyapunov . , 1899, .


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. , Chebyshev Markov, , . . [1]

, Lyapunov

. , , . , . . , . [1] 1884, ( ) 1892, ( ) 1897, Sur certaines qui se rattachent au probleme de Dirichlet 1901, Novelle forme du thorme sur la limite de probabilit 1901, Sur un thorme du Calcul des probabilits 1902, Sur une srie dans la thorie des diffrentielles linaires du

priodiques 1903, Recherches dans la thorie de la des clestes 1904, Sur l' de Clairaut et les plus Generales de la thorie de la des plantes

Prokopy Lyapunov

Prokopy Lyapunov Rurikid ...Prokopy Lyapunov (: ) ( 1611 ) Rurikid, . , Prokopy Zakhary Lyapunov I.

1606, Bolotnikov . 1606, Lyapunov IV. , Lyapunov dvoryanin Boyar (1607) . 1608-1610, Lyapunov Ryazan II. 1610, Lyapunov IV.

1611, Lyapunov, E , . 1611, . 1611,Lyapunov . 30, , . , 1 1611OS Dmitry Pozharsky, 1612.

Zakhary Lyapunov Zakhary Lyapunov (: ) (; - 1612) 17 , Prokopy Lyapunov. 1605, Zakhary Lyapunov . 1606, Bolotnikov 1606-1607. 1607, Vasily Shuisky dvoryane Dmitri II.


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1610, Zachary Lyapunov VasilyShuisky . 1610, , III Vasa Wladislaus . , Kuzma Minin

Pozharsky

( ? : ,Dimitrii, Dimitriy, Dimitry, Dmitri, Dmitrii, Dmitry) 21 , 1605 17 , 1606 Dimitriy Ioannovich ( ). Dmitriy II. ,tsarevitch Dmitriy Ivanovich, 1591. Dmitriy Uglich Otrepyev, . 1600, . , , , Ostrogsky , , - , Ruthenian, Wisniowieckis. Micha Winiowiecki , , .

Dmitriy , Stefan Batory, 1575 - 1586. , Dmitriy blurted , . Dmitriy , , . , , Wisniowiecki. Dmitriy tsarevitch. Dmitriy . Dmitriy, Adam Winiowiecki, Ryski, Jan Sapieha . 1604, Dmitriy Vasa . , . , Dmitriy 17 1604 ClaudioRangoni . Mniszech, , Jerzy Mniszech. Mniszech Pskov, , Novhorod-Siverskyi.

' False. , Grigory Otrepyev( Yury Otrepyev? ), . , , . Dmitriy, .

Dmitriy , , 3500 . 1604.


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Boris, , . Dmitriy ? , Chernigov ( Chernihiv), Putivl (Putyvl), Sevsk, , . Dmitriy , (13 1605) .Chernihiv Rus'- (907) (), establishemt Khazar Khaganate, 9 . 10 , . Grave, , 19 . , . [2] 11 Chernigov, Kievan Grand Princes, . Severian , , Tmutarakan. Chernihiv, 25.000, 1239, , . 1036 . 1353. , Meli Giray 1482 1497 , (1408-1420 1503), - (1618-1648 ), 1623 1635 Chernihiv Voivodeship.

17 , Khmelnytsky . Hetman Chernihiv Chernihiv ( ). 1667 Andrusovo , Chernihiv Hetmanate. Hetmanate, . , , Chernihiv namestnichestvo () ( 1782), Malorosiyskaya ( 1797) Chernigov ( 1808 ). 1897 Chernihiv 11.000 27.006. .

. Chernihiv 1.321 , 404 seamstresses, . 69 (-, Teamsters. , [3]. . Dmitriy, 1 , ', . 20 Dmitriy , 21 , .

Putyvl Siverian , Putyvl 1146 Chernigov -Seversky . Yaroslavna Putyvl


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Lay Igor Prince Igor. Vedrosha 1500, Putyvl . , Bolotnikov Dmitry .Putyvl guberniya ,

. Sydir Kovpak . Putivl Molchansky , 17 . , , 1590s , , Paul 1654 . , . , Putivl (1735-1737) , , 1617 . 17

? , 1700. '

Vasa Nevrev (1874)

Nagaya, . Godunova, . ,

- Shuiskys, Golitsins Romanovs - .Filaret ( Romanov), . , , .Dmitriy . , , . , Dmitriy - . . , , ', . 8 1606, Dmitriy Mniszech .

, . Dmitriy , . , . '

. , (). , parsuna, 16 ( )

3 1533 - 28 [O.S. 18 ] 1584

16 1547


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Vasili III

m. 1547, . 1560

Temrjukovnam. 1561, . 1569Marfa Sobakinm. 1571, . 1571Anna Koltovskim. 1572, ann. 1574Anna Vasilchikovm. 1575, . 1576-77Vasilisa Melentevm. 1579, ann. 1579 Dolgorukim. 1580, 1580 Nagaya

m. 1581Tsarevna Tsarevna Dmitri Ivanovich Ivanovich IvanTsarevna Ivanovich Feodor Vasili Ivanovich Dmitri Ivanovich Shestova ()

Oik Rurik

Vasili III

Glinskaya

25, 1530Kolomenskoye,

18 [O.S. 18 ] 1584 ( 53)

Kelmisvi Chapel,

(: , ( ), Chetvyorty, ), (Ivan Grozny : ( )) (25 1530, - 28 [OS 18] 1584, [1], ) 1533. , , . [2] [3] [4] , . : ? . Ivan Ivanovich ( , ), Tsardom : ,


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, [5] ' . Khanates , Astrakhan, , multiconfessional 1 , 130 [6]. , 1525

( ). , . Ivan . , Glinskaya , [7], . Shuisky 1544. , , Shuisky Belsky .Ivan 16 1547. 1547, ,

. ( sudebnik), ( streltsy), [8] Zemsky Sobor , , , ( Chosen ), , . , , . , ( Fedorov Mstislavets ).

IV Vasnetsov , 1897 ( , ) 1547 Hans Schlitte, , . Lbeck Livonia. 1550 Livonia.
http://en.wikipedia.org/wiki/File:Vasnetsov_Ioann_4.jpg


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.Ivan , . 1552 , , [9] . 1556,

. multiconfessional . . , , 1558 Gennady, , , , . , Smolensk Vasily Poznyakov. Poznyakov , , , , [10].

. O , Postnik Yakovlev, , . , Yakovlev 1560s, Vasilii 1588, , , , .

Romanovna. 1875 Grigory SemyonovichSedov (1836-1886)

, , , 1553 , Romanovna 1560. Ivan , . , , . , . . , Gorbatyi-Shuisky.

1565 Oprichnina . Oprichnina ( ) , Oprichniki. Oprichnina (), , ., ' , ? .


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, 16 , 1581 , 1885( , ) . Khan devlet Giray 1571, Yermak , ,

, , ,, Livonian . Livonian , . 1560s , - , , , Hanseatic League . . 10.000 Novgorod. 1570 600-1000 . [11]

, Kurbsky, , Velikiye . .

Oprichnina , . , . , Oprichniks Malyuta Skuratov . , Livonia. . . , Oprichniks , . . [12] 60,000 1570? [12]

[13] [14] [14]. , 1.500 () . . ( 1560s 10,000-20,000.) [15]

Basilius Magnus Imperator Russic, Dux Moscovic Ortelius , 1574

Jerome horsey Litovchenko Alexander (1875) , 1579, Muscovian , ( - Wars). . , , Oprichnina , , Stefan Batory, , (1576). . , Batory 1579-1581, Livonia Muscovian . 1579, Polotsk 22.000 . , 1580,


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29.000- . , Pskov 1581 100.000 .

Frederick , . John 1580 Livonia. 1577 - 1582.

- Ducatus Ultradunensis 1582. Magnusvon Lyffland 1583, Courland . Saaremaa, 1585. 1598, Livonia : Wenden Voivodeship (Wojewdztwo wendeskie, Kie) Dorpat Voivodeship (Wojewdztwo dorpackie, Dorpat) Parnawa Voivodeship (Wojewdztwo parnawskie, Parnawa) 1581, -- , . , , , , , () .

, 16 ,1581 .

Gerasimov

. Rurik . Schwarz Grigorievich Vyacheslav (1861) , ' BogdanBelsky [16], Belsky [] 18 1584. [16] , . , [17].

: Pskovo-Pechorsky . Klavdiy .DS Mirsky Ivan " ". ( ) . , . , . polemicist Kurbsky : " , ;" . upbraiding , , ". [19] , Keenan 17 . , , , , Fennell Ruslan Skrynnikov . 16 , Kurbsky invectives .


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Kirillo-Belozersky , unascetic , , . ascetism .

, , , . - , ( ), , , . , .

Ancestors of Ivan IV of Russia [hide]

16. Vasily I of Moscow

8. Vasily II of Moscow

17. Sophia of Lithuania

4. Ivan III of Russia

18. Yaroslav of Borovsk

9. Maria of Borovsk

19. Maria GoltiayevaKoshkina

2. Vasili III of Russia

20. Manuel II Palaiologos

10. Thomas Palaiologos
http://en.wikipedia.org/wiki/Vasily_I_of_Moscowhttp://en.wikipedia.org/wiki/Vasily_I_of_Moscowhttp://en.wikipedia.org/wiki/Vasily_II_of_Moscowhttp://en.wikipedia.org/wiki/Vasily_II_of_Moscowhttp://en.wikipedia.org/wiki/Sophia_of_Lithuaniahttp://en.wikipedia.org/wiki/Ivan_III_of_Russiahttp://en.wikipedia.org/wiki/Ivan_III_of_Russiahttp://en.wikipedia.org/w/index.php?title=Yaroslav_of_Borovsk&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Yaroslav_of_Borovsk&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Maria_of_Borovsk&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Maria_Goltiayeva_Koshkina&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Maria_Goltiayeva_Koshkina&action=edit&redlink=1http://en.wikipedia.org/wiki/Vasili_III_of_Russiahttp://en.wikipedia.org/wiki/Vasili_III_of_Russiahttp://en.wikipedia.org/wiki/Manuel_II_Palaiologoshttp://en.wikipedia.org/wiki/Thomas_Palaiologoshttp://en.wikipedia.org/wiki/Thomas_Palaiologoshttp://en.wikipedia.org/wiki/Vasily_I_of_Moscowhttp://en.wikipedia.org/wiki/Vasily_II_of_Moscowhttp://en.wikipedia.org/wiki/Sophia_of_Lithuaniahttp://en.wikipedia.org/wiki/Ivan_III_of_Russiahttp://en.wikipedia.org/w/index.php?title=Yaroslav_of_Borovsk&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Maria_of_Borovsk&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Maria_Goltiayeva_Koshkina&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Maria_Goltiayeva_Koshkina&action=edit&redlink=1http://en.wikipedia.org/wiki/Vasili_III_of_Russiahttp://en.wikipedia.org/wiki/Manuel_II_Palaiologoshttp://en.wikipedia.org/wiki/Thomas_Palaiologos


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21. Helena Draga

5. Sophia (Zoe)Palaiologina

22. Centurione II Zaccaria

11. Catherine Zaccaria

23. Creusa Tocco

1. Ivan IV of Russia

24. Borys Ivanovich Glinsky

12. Lev BorysevichGlinsky

25. N. widow of IvanKorybutovich

6. Vasili Lvovich Glinsky
http://en.wikipedia.org/wiki/Helena_Draga%C5%A1http://en.wikipedia.org/wiki/Sophia_Palaiologinahttp://en.wikipedia.org/wiki/Sophia_Palaiologinahttp://en.wikipedia.org/wiki/Centurione_II_Zaccariahttp://en.wikipedia.org/w/index.php?title=Catherine_Zaccaria&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Vasili_Lvovich_Glinsky&action=edit&redlink=1http://en.wikipedia.org/wiki/Helena_Draga%C5%A1http://en.wikipedia.org/wiki/Sophia_Palaiologinahttp://en.wikipedia.org/wiki/Sophia_Palaiologinahttp://en.wikipedia.org/wiki/Centurione_II_Zaccariahttp://en.wikipedia.org/w/index.php?title=Catherine_Zaccaria&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Vasili_Lvovich_Glinsky&action=edit&redlink=1


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3. Elena Glinskaya

28. Jaksa

14. Stefan Iakshich

7. Anna of Serbia

15. N. Belmosevic

Cossacks
http://en.wikipedia.org/wiki/Elena_Glinskayahttp://en.wikipedia.org/wiki/Elena_Glinskaya


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(: , ? : , Kozaky? : Kozacy) . [1] . 15 , Zaporozhian , " " . 16, Don

. , . Zaporozhian Sich . -, Hetmanate, Bohdan Khmelnytsky 17 . , Pereyaslavl . Don , , , , Terek . 18

, . Stenka Razin, Kondraty Bulavin Yemelyan Pugachev. , , Zaporozhian Sich 1775. 18, ? ( ) , Russo -. . 19 . White , White. . , , .

, , repressionary . , . , , . , , .


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Don Ural TerekKuban Orenburg Baikal Amur Semirechye UssuriZaporozhia

(Sich) Nekrasov

Kosiski Nalyvaiko Khmelnytsky Hadiach Hetmanate Rebellion Bulavin Pugachev 1 Decossackization SS XV 1stDivision

Bohdan Khmelnytsky Sahaidachny Vyhovsky Doroshenko Mazepa Sirko Pugachev Yemelyan Stenka Razin Shkuro Krasnov Yermak Walikhanuli Shokan Timofeyevich

Hetman Kontusz Papakhi Plastun Szabla Shashka Stanitsa

Yesaul

, . 13 , . , Cumans Circassian Kassaks ( Kassogs) .Proto- 13 . 1261 Ruthenian . 16 . Don , 1380, [ ]. 15 , , , (, .., , )

16 , . Zaporizhia, , , Zaporozhian Sich. , Zaporozhian , 1649. , , Nogai, . Cherkassk, . (Kozacy) (Naaybklr). , - .


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[] Zaporozhian : Zaporozhian Zaporozhian . Zaporozhian ."Bohdan Khmelnytsky Toay Lviv, , 1885,

. Matejko Zaporozhian , , . 15 17 , boyar, - . Zaporozhian , - , . Khmelnytsky 17 Zaporozhian , Hetmanate, , Hetmans

. 18 Zaporozhian . . 1828 Danubians . [] Kuban , . Zaporozhians , , . -, , - . 1539 , ' : , ." 1549, , , , , . , - , . 16 , - , Zaporozhian , , - , . [8] 1699. 16 , - , , . 16 , . , , . , , . ,, ,


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, . 1615 1625, , .

[9] - , . , , . , , . , . . , , . - - , Cecora 1633-1634 .

- . szlachta Zaporozhian . szlachta

, - ( Ruthenian ) . - . , -, -.


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szlachta - 17 . , , :

Khmelnytsky 1648. , - 100 . 1654 Pereyaslav , starshyna () , , [10]. , , - - Ruthenian- 1658 Hadiach, starshyna, Hetman

Vyhovsky. [11] starshyna , , --? .

. Brandt Jzef.

Zaporozhian : Hetmanate, Zaporizhia. , Catherine II, 18 . Hetmanate Little , Zaporizhia . 1775 Zaporozhian Solovky .

,

Zaporozhian Sich, Danuvbe . . .

( ), Kuban.

, 19 .


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, , 1778 12.000 . . , , , . , , , . , 1787-1792, . 1828 Berdyansk . 1860 .[]

1814.


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/ Ruthenian - , , Pereyaslavl. . ,

, (), . 1444. 16 , ( ) ( Vasily Klyuchevsky, , VOL.2) . , , , , , . 16 , ,

, Nogai Horde . , shashka, . ( Yermak Timofeyevich), , 16 19 . , . 1648 Semyon Dezhnyov . 17, 18 19 ( , - , ). , . . , ."[12] - , . , , , , , . 1814. , 1812 .


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Yermak, . , , , . Zaporozhian, 18 .

( ) - . ' 19 , . . , , , . 1840 , , Astrakhan, Little ,

, , Ural, , Mesherya, , , , Tomsk, Yeniseisk, , Sabaikal, Yakutskand voiskos. 1890 Ussuri, Semirechensk Amur , [

, 1905 , 1905. Imperial , 20 , - . Command, , hussars, . [19] - . , , . 1917, , . , ( Konvoi) . 19 , , ( 1909). , . 4,5 , .

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118a Liapunov Liapis Origin Gr

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