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 journalArticlepeer-review

32 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 languageEnglish
Pages (from-to)435-460
Number of pages26
JournalRegular and Chaotic Dynamics
Volume19
Issue number4
DOIs
StatePublished - 1 Jan 2014
Externally publishedYes

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

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

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