Ergodic perturbations of degenerate integrable hamiltonian systems

Anatoly Katok

Research output: Contribution to journalArticle

49 Citations (Scopus)

Abstract

Hamiltonian systems arbitrarily close in the Cr topology (r= 1, 2, …) to a given integrable degenerate Hamiltonian system of class C which generate an ergodic flow on each manifold of constant energy are constructed. Applications: Small perturbations of a system generated by independent oscillators and Finsler metrics close to standard Riemannian metrics on symmetric spaces of rank 1.

Original languageEnglish (US)
Pages (from-to)535-571
Number of pages37
JournalMathematics of the USSR - Izvestija
Volume7
Issue number3
DOIs
StatePublished - Jun 30 1973

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Integrable Hamiltonian System
Hamiltonian Systems
Perturbation
Finsler Metric
Riemannian Metric
Symmetric Spaces
Small Perturbations
Topology
Energy
Class
Standards

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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abstract = "Hamiltonian systems arbitrarily close in the Cr topology (r= 1, 2, …) to a given integrable degenerate Hamiltonian system of class C which generate an ergodic flow on each manifold of constant energy are constructed. Applications: Small perturbations of a system generated by independent oscillators and Finsler metrics close to standard Riemannian metrics on symmetric spaces of rank 1.",
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Ergodic perturbations of degenerate integrable hamiltonian systems. / Katok, Anatoly.

In: Mathematics of the USSR - Izvestija, Vol. 7, No. 3, 30.06.1973, p. 535-571.

Research output: Contribution to journalArticle

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