Scientific heritage of L.P. Shilnikov

Valentin S. Afraimovich; Sergey V. Gonchenko; Lev M. Lerman; Andrey L. Shilnikov; Dmitry V. Turaev

doi:10.1134/S1560354714040017

Scientific heritage of L.P. Shilnikov

Valentin S. Afraimovich, Sergey V. Gonchenko, Lev M. Lerman, Andrey L. Shilnikov, Dmitry V. Turaev

Research output: Contribution to journal › Article › peer-review

38 Scopus citations

Abstract

This is the first part of a review of the scientific works of L.P. Shilnikov. We group his papers according to 7 major research topics: bifurcations of homoclinic loops; the loop of a saddle-focus and spiral chaos; Poincare homoclinics to periodic orbits and invariant tori, homoclinic in noautonous and infinite-dimensional systems; Homoclinic tangency; Saddlenode bifurcation—quasiperiodicity-to-chaos transition, blue-sky catastrophe; Lorenz attractor; Hamiltonian dynamics. The first two topics are covered in this part. The review will be continued in the further issues of the journal.

Original language	English
Pages (from-to)	435-460
Number of pages	26
Journal	Regular and Chaotic Dynamics
Volume	19
Issue number	4
DOIs	https://doi.org/10.1134/S1560354714040017
State	Published - 1 Jan 2014
Externally published	Yes

Keywords

Global bifurcations
Homoclinic chaos
Homoclinic loop
Hyperbolic set
Lorenz attractor
Saddle-focus
Saddle-node
Saddle-saddle
Spiral chaos
Strange attractor

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematics (miscellaneous)
Modeling and Simulation
Mathematical Physics
Mechanical Engineering
Applied Mathematics

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10.1134/S1560354714040017

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title = "Scientific heritage of L.P. Shilnikov",

abstract = "This is the first part of a review of the scientific works of L.P. Shilnikov. We group his papers according to 7 major research topics: bifurcations of homoclinic loops; the loop of a saddle-focus and spiral chaos; Poincare homoclinics to periodic orbits and invariant tori, homoclinic in noautonous and infinite-dimensional systems; Homoclinic tangency; Saddlenode bifurcation—quasiperiodicity-to-chaos transition, blue-sky catastrophe; Lorenz attractor; Hamiltonian dynamics. The first two topics are covered in this part. The review will be continued in the further issues of the journal.",

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AU - Afraimovich, Valentin S.

AU - Gonchenko, Sergey V.

AU - Lerman, Lev M.

AU - Shilnikov, Andrey L.

AU - Turaev, Dmitry V.

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KW - Global bifurcations

KW - Homoclinic chaos

KW - Homoclinic loop

KW - Hyperbolic set

KW - Lorenz attractor

KW - Saddle-focus

KW - Saddle-node

KW - Saddle-saddle

KW - Spiral chaos

KW - Strange attractor

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Scientific heritage of L.P. Shilnikov

Abstract

Keywords

ASJC Scopus subject areas

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