可逆动力系统中的对称同斜缠结具有正拓扑熵

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-02-05 DOI:10.1016/j.aim.2025.110131

A.J. Homburg , J.S.W. Lamb , D.V. Turaev

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引用次数: 0

摘要

考虑R2n中的可逆向量场，使得对合可逆对称的不动点集是n维的。设该系统在法向上具有光滑的鞍型单参数对称周期轨道族。我们证明了当这类周期轨道的稳定流形和不稳定流形具有强横向相交时，拓扑熵是正的。

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Symmetric homoclinic tangles in reversible dynamical systems have positive topological entropy

We consider reversible vector fields in

R^{2 n}

such that the set of fixed points of the involutory reversing symmetry is n-dimensional. Let such system have a smooth one-parameter family of symmetric periodic orbits which is of saddle type in normal directions. We establish that the topological entropy is positive when the stable and unstable manifolds of this family of periodic orbits have a strongly-transverse intersection.

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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.