Discovery of closed orbits of dynamical systems with the use of computers

Ja G. Sinai; E. B. Vul

doi:10.1007/BF01014428

Discovery of closed orbits of dynamical systems with the use of computers

Ja G. Sinai
, E. B. Vul

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

17 Scopus citations

Abstract

In this paper we derive a general criterion which can be used for the discovery with the use of a computer of closed orbits of systems of ordinary differential equations. We apply this criterion to the Lorenz model and show rigorously the existence of a closed orbit for the case under consideration. In a subsequent paper we shall show how the stable manifold of this orbit determines the boundary of the stochastic attractor.

Original language	English (US)
Pages (from-to)	27-47
Number of pages	21
Journal	Journal of Statistical Physics
Volume	23
Issue number	1
DOIs	https://doi.org/10.1007/BF01014428
State	Published - Jul 1980

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

Poincaré mapping
attractor
closed orbit
linear system of equations in variations

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10.1007/BF01014428

Cite this

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title = "Discovery of closed orbits of dynamical systems with the use of computers",

abstract = "In this paper we derive a general criterion which can be used for the discovery with the use of a computer of closed orbits of systems of ordinary differential equations. We apply this criterion to the Lorenz model and show rigorously the existence of a closed orbit for the case under consideration. In a subsequent paper we shall show how the stable manifold of this orbit determines the boundary of the stochastic attractor.",

keywords = "Poincar{\'e} mapping, attractor, closed orbit, linear system of equations in variations",

author = "Sinai, \{Ja G.\} and Vul, \{E. B.\}",

year = "1980",

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T1 - Discovery of closed orbits of dynamical systems with the use of computers

AU - Sinai, Ja G.

AU - Vul, E. B.

PY - 1980/7

Y1 - 1980/7

N2 - In this paper we derive a general criterion which can be used for the discovery with the use of a computer of closed orbits of systems of ordinary differential equations. We apply this criterion to the Lorenz model and show rigorously the existence of a closed orbit for the case under consideration. In a subsequent paper we shall show how the stable manifold of this orbit determines the boundary of the stochastic attractor.

AB - In this paper we derive a general criterion which can be used for the discovery with the use of a computer of closed orbits of systems of ordinary differential equations. We apply this criterion to the Lorenz model and show rigorously the existence of a closed orbit for the case under consideration. In a subsequent paper we shall show how the stable manifold of this orbit determines the boundary of the stochastic attractor.

KW - Poincaré mapping

KW - attractor

KW - closed orbit

KW - linear system of equations in variations

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U2 - 10.1007/BF01014428

DO - 10.1007/BF01014428

M3 - Article

AN - SCOPUS:0002929195

SN - 0022-4715

VL - 23

SP - 27

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JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 1

ER -

Discovery of closed orbits of dynamical systems with the use of computers

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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