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1

Hyperbolic properties of four-dimensional symplectic mappings with a structurally unstable trajectory homoclinic to a fixed point of the saddle-focus type

S. V. Gonchenko, L. P. Shil’nikov

Journal:

Differential Equations

Year:

2000

Language:

english

File:

PDF, 846 KB

english, 2000

2

Generalized Hénon Map and Bifurcations of Homoclinic Tangencies

Gonchenko, V. S., Kuznetsov, Yu. A., Meijer, H. G. E.

Journal:

SIAM Journal on Applied Dynamical Systems

Year:

2005

Language:

english

File:

PDF, 820 KB

english, 2005

3

Bifurcations of three-dimensional diffeomorphisms with non-simple quadratic homoclinic tangencies and generalized Hénon maps

S. V. Gonchenko, V. S. Gonchenko, J. C. Tatjer

Journal:

Regular and Chaotic Dynamics

Year:

2007

Language:

english

File:

PDF, 1.19 MB

english, 2007

4

On a homoclinic origin of Hénon-like maps

S. V. Gonchenko, V. S. Gonchenko, L. P. Shilnikov

Journal:

Regular and Chaotic Dynamics

Year:

2010

Language:

english

File:

PDF, 637 KB

english, 2010

5

Invariants of Ω-conjugacy of diffeomorphisms with a nongeneric homoclinic trajectory

S. V. Gonchenko, L. P. Shil'nikov

Journal:

Ukrainian Mathematical Journal

Year:

1990

Language:

english

File:

PDF, 561 KB

english, 1990

6

ON MODULI OF SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC POINCARÉ CURVE

Gonchenko, S V, Shil'nikov, L P

Journal:

Izvestiya Mathematics

Year:

1993

Language:

english

File:

PDF, 461 KB

english, 1993

7

Homoclinic tangencies of arbitrarily high orders in conservative and dissipative two-dimensional maps

Gonchenko, Sergey, Turaev, Dmitry, Shilnikov, Leonid

Journal:

Year:

2007

Language:

english

File:

PDF, 656 KB

english, 2007

8

Chaotic Dynamics and Multistability in the Nonholonomic Model of a Celtic Stone

Gonchenko, A. S., Gonchenko, S. V., Kazakov, A. O., Samylina, E. A.

Journal:

Radiophysics and Quantum Electronics

Year:

2019

Language:

english

File:

PDF, 863 KB

english, 2019

9

On the Region of Existence of a Discrete Lorenz Attractor in the Nonholonomic Model of a Celtic Stone

Gonchenko, A. S., Samylina, E. A.

Journal:

Radiophysics and Quantum Electronics

Year:

2019

Language:

english

File:

PDF, 933 KB

english, 2019

10

On the Region of Existence of a Discrete Lorenz Attractor in the Nonholonomic Model of a Celtic Stone

Gonchenko, A. S., Samylina, E. A.

Journal:

Radiophysics and Quantum Electronics

Year:

2019

File:

PDF, 933 KB

2019

11

Scenarios of hyperchaos occurrence in 4D RÃ¶ssler system

Stankevich, N., Kazakov, A., Gonchenko, S.

Journal:

Chaos An Interdisciplinary Journal of Nonlinear Science

Year:

2020

File:

PDF, 11.43 MB

2020

12

On models with non-rough Poincaré homoclinic curves

S.V. Gonchenko, L.P. Shil'nikov, D.V. Turaev

Journal:

Physica D: Nonlinear Phenomena

Year:

1993

Language:

english

File:

PDF, 950 KB

english, 1993

13

Quasiattractors and homoclinic tangencies

S.V. Gonchenko, L.P. Shil'nikov, D.V. Turaev

Journal:

Computers & Mathematics with Applications

Year:

1997

Language:

english

File:

PDF, 2.78 MB

english, 1997

14

Stable periodic motions in systems close to a structurally unstable homoclinic curve

S. V. Gonchenko

Journal:

Mathematical Notes

Year:

1983

Language:

english

File:

PDF, 408 KB

english, 1983

15

On dynamic properties of diffeomorphisms with homoclinic tangency

S. V. Gonchenko, D. V. Turaev, L. P. Shil’nikov

Journal:

Journal of Mathematical Sciences

Year:

2005

Language:

english

File:

PDF, 268 KB

english, 2005

16

On Two-Dimensional Area-Preserving Maps with Homoclinic Tangencies that Have Infinitely Many Generic Elliptic Periodic Points

S. V. Gonchenko, L. P. Shilnikov

Journal:

Journal of Mathematical Sciences

Year:

2005

Language:

english

File:

PDF, 186 KB

english, 2005

17

On Bifurcations of Three-Dimensional Diffeomorphisms with a Homoclinic Tangency to a “Neutral” Saddle Fixed Point

V. S. Gonchenko, I. I. Ovsyannikov

Journal:

Journal of Mathematical Sciences

Year:

2005

Language:

english

File:

PDF, 127 KB

english, 2005

18

Bifurcations of systems with structurally unstable homoclinic orbits and moduli of ω-equivalence

S.V. Gonchenko, L.P. Shil'nikov, O.V. Sten'kin, D.V. Turaev

Journal:

Computers & Mathematics with Applications

Year:

1997

Language:

english

File:

PDF, 2.26 MB

english, 1997

19

Homoclinic tangencies of arbitrarily high order in conservative two-dimensional maps

S. V. Gonchenko, D. V. Turaev, L. P. Shil’nikov

Journal:

Doklady Mathematics

Year:

2006

Language:

english

File:

PDF, 186 KB

english, 2006

20

On bifurcations of systems with homoclinic loops to a saddle-focus with saddle index ½

V. S. Gonchenko, L. P. Shil’nikov

Journal:

Doklady Mathematics

Year:

2007

Language:

english

File:

PDF, 179 KB

english, 2007

21

On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors

S. V. Gonchenko, L. P. Shilnikov, D. V. Turaev

Journal:

Regular and Chaotic Dynamics

Year:

2009

Language:

english

File:

PDF, 624 KB

english, 2009

22

Shilnikov’s Cross-map method and hyperbolic dynamics of three-dimensional Hénon-like maps

S. Gonchenko, M. -Ch. Li

Journal:

Regular and Chaotic Dynamics

Year:

2010

Language:

english

File:

PDF, 387 KB

english, 2010

23

On cascades of elliptic periodic points in two-dimensional symplectic maps with homoclinic tangencies

M. S. Gonchenko, S. V. Gonchenko

Journal:

Regular and Chaotic Dynamics

Year:

2009

Language:

english

File:

PDF, 1.01 MB

english, 2009

24

Leonid Pavlovich Shilnikov. On his 75thbirthday

V. S. Afraimovich, L. M. Lerman, S. V. Gonchenko

Journal:

Regular and Chaotic Dynamics

Year:

2010

Language:

english

File:

PDF, 8.74 MB

english, 2010

25

Homoclinic Tangencies of an Arbitrary Order in Newhouse Domains

S. V. Gonchenko, D. V. Turaev, L. P. Shil'nikov

Journal:

Journal of Mathematical Sciences

Year:

2001

Language:

english

File:

PDF, 720 KB

english, 2001

26

Stable Periodic Trajectories of Two-Dimensional Diffeomorphisms Close to a Diffeomorphism with a Structurally Unstable Heteroclinic Contour

S. V. Gonchenko, A. S. Markichev, A. E. Shatalin

Journal:

Differential Equations

Year:

2001

Language:

english

File:

PDF, 300 KB

english, 2001

27

Arithmetic properties of topological invariants of systems with nonstructurally-stable homoclinic trajectories

S. V. Gonchenko, L. P. Shil'nikov

Journal:

Ukrainian Mathematical Journal

Year:

1987

Language:

english

File:

PDF, 552 KB

english, 1987

28

On the effect of invisibility of stable periodic orbits at homoclinic bifurcations

S.V. Gonchenko, I.I. Ovsyannikov, D. Turaev

Journal:

Physica D: Nonlinear Phenomena

Year:

2012

Language:

english

File:

PDF, 464 KB

english, 2012

29

On dynamic properties of diffeomorphisms with homoclinic tangency

S. V. Gonchenko, D. V. Turaev, L. P. Shil’nikov

Journal:

Journal of Mathematical Sciences

Year:

2005

Language:

english

File:

PDF, 344 KB

english, 2005

30

10.1070/RD2006v011n02ABEH000346

Gonchenko, S.V., Schneider, K.R., Turaev, D.V.

Journal:

Regular and Chaotic Dynamics

Year:

2006

Language:

english

File:

PDF, 557 KB

english, 2006

31

Attractors and repellers near generic elliptic points of reversible maps

Gonchenko, S. V., Lamb, J. S. W., Rios, I., Turaev, D.

Journal:

Doklady Mathematics

Year:

2014

Language:

english

File:

PDF, 212 KB

english, 2014

32

Richness of chaotic dynamics in nonholonomic models of a celtic stone

Gonchenko, Alexander S., Gonchenko, Sergey V., Kazakov, Alexey O.

Journal:

Regular and Chaotic Dynamics

Year:

2013

Language:

english

File:

PDF, 1.58 MB

english, 2013

33

Simple Scenarios of Onset of Chaos in Three-Dimensional Maps

Gonchenko, Alexander, Gonchenko, Sergey, Kazakov, Alexey, Turaev, Dmitry

Journal:

International Journal of Bifurcation and Chaos

Year:

2014

Language:

english

File:

PDF, 4.59 MB

english, 2014

34

Examples of Lorenz-like Attractors in Hénon-like Maps

Gonchenko, S.V., Gonchenko, A.S., Ovsyannikov, I.I., Turaev, D.V., Lerman, L., Turaev, D., Vougalter, V., Zaks, M.

Journal:

Mathematical Modelling of Natural Phenomena

Year:

2013

Language:

english

File:

PDF, 1.64 MB

english, 2013

35

Birth of discrete Lorenz attractors at the bifurcations of 3D maps with homoclinic tangencies to saddle points

Gonchenko, Sergey V., Ovsyannikov, Ivan I., Tatjer, Joan C.

Journal:

Regular and Chaotic Dynamics

Year:

2014

Language:

english

File:

PDF, 395 KB

english, 2014

36

Scientific heritage of L.P. Shilnikov

Valentin S. Afraimovich,Sergey V. Gonchenko,Lev M. Lerman…

Journal:

Regular and Chaotic Dynamics

Year:

2014

Language:

english

File:

PDF, 4.70 MB

english, 2014

37

On bifurcations of multidimensional diffeomorphisms having a homoclinic tangency to a saddle-node

Serey V. Gonchenko,Olga V. Gordeeva,Valery I. Lukyanov…

Journal:

Regular and Chaotic Dynamics

Year:

2014

Language:

english

File:

PDF, 803 KB

english, 2014

38

Editorial — Leonid Pavlovich Shilnikov

Shilnikov, A. L., Turaev, D. V., Lerman, L. M., Afraimovich, V. S., Gonchenko, S. V., Belyakov, L. A.

Journal:

International Journal of Bifurcation and Chaos

Year:

2014

Language:

english

File:

PDF, 781 KB

english, 2014

39

Exponentially Small Lower Bounds for the Splitting of Separatrices to Whiskered Tori with Frequencies of Constant Type

Delshams, Amadeu, Gonchenko, Marina, Gutiérrez, Pere

Journal:

International Journal of Bifurcation and Chaos

Year:

2014

Language:

english

File:

PDF, 538 KB

english, 2014

40

ON THE STRUCTURE OF 1 : 4 RESONANCES IN HÉNON MAPS

GONCHENKO, M. S.

Journal:

International Journal of Bifurcation and Chaos

Year:

2005

Language:

english

File:

PDF, 505 KB

english, 2005

41

ON GEOMETRICAL PROPERTIES OF TWO-DIMENSIONAL DIFFEOMORPHISMS WITH HOMOCLINIC TANGENCIES

GONCHENKO, S.V., SHIL’NIKOV, L.P.

Journal:

International Journal of Bifurcation and Chaos

Year:

1995

Language:

english

File:

PDF, 668 KB

english, 1995

42

THREE-DIMENSIONAL HÉNON-LIKE MAPS AND WILD LORENZ-LIKE ATTRACTORS

GONCHENKO, S. V., OVSYANNIKOV, I. I., SIMÓ, C., TURAEV, D.

Journal:

International Journal of Bifurcation and Chaos

Year:

2005

Language:

english

File:

PDF, 3.38 MB

english, 2005

43

GENERALIZED HÉNON MAPS AND SMALE HORSESHOES OF NEW TYPES

GONCHENKO, SERGEY, LI, MING-CHIA, MALKIN, MIKHAIL

Journal:

International Journal of Bifurcation and Chaos

Year:

2008

Language:

english

File:

PDF, 949 KB

english, 2008

44

Abundance of attracting, repelling and elliptic periodic orbits in two-dimensional reversible maps

Delshams, A, Gonchenko, S V, Gonchenko, V S, Lázaro, J T, Sten'kin, O

Journal:

Year:

2013

Language:

english

File:

PDF, 65 KB

english, 2013

45

Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio

Delshams, Amadeu, Gonchenko, Marina, Gutiérrez, Pere

Journal:

Regular and Chaotic Dynamics

Year:

2014

Language:

english

File:

PDF, 1.65 MB

english, 2014

46

On bifurcations of area-preserving and nonorientable maps with quadratic homoclinic tangencies

Delshams, Amadeu, Gonchenko, Marina, Gonchenko, Sergey V.

Journal:

Regular and Chaotic Dynamics

Year:

2014

Language:

english

File:

PDF, 976 KB

english, 2014

47

Leonid Pavlovich Shil'nikov (obituary)

Anosov, Dmitry V, Afraimovich, Valentin S, Bunimovich, Leonid A, Gonchenko, Sergei V, Grines, Vyacheslav Z, Ilyashenko, Yulij S, Katok, Anatolii B, Kashchenko, Sergey A, Kozlov, Valerii V, Lerman, Lev

Journal:

Russian Mathematical Surveys

Year:

2012

Language:

english

File:

PDF, 101 KB

english, 2012

48

Richness of dynamics and global bifurcations in systems with a homoclinic figure-eight

Gonchenko, S V, Simó, C, Vieiro, A

Journal:

Year:

2013

Language:

english

File:

PDF, 6.65 MB

english, 2013

49

Complexity in the bifurcation structure of homoclinic loops to a saddle-focus

Gonchenko, S V, Turaev, D V, Gaspard, P, Nicolis, G

Journal:

Year:

1997

Language:

english

File:

PDF, 909 KB

english, 1997

50

On dynamical properties of multidimensional diffeomorphisms from Newhouse regions: I

Gonchenko, S V, Shilnikov, L P, Turaev, D V

Journal:

Year:

2008

Language:

english

File:

PDF, 338 KB

english, 2008

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