Homoclinic points for convex billiards

Zhihong Xia; Pengfei Zhang

doi:10.1088/0951-7715/27/6/1181

Homoclinic points for convex billiards

Zhihong Xia, Pengfei Zhang

Mathematics

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

8 Scopus citations

Abstract

In this paper we investigate some generic properties of a billiard system on a convex table. We show that C^∞ generically, every hyperbolic periodic point admits some homoclinic orbit.

Original language	English (US)
Pages (from-to)	1181-1192
Number of pages	12
Journal	Nonlinearity
Volume	27
Issue number	6
DOIs	https://doi.org/10.1088/0951-7715/27/6/1181
State	Published - Jun 2014

Keywords

Moser stable
convex billiards
generic properties
heteroclinic connection
homoclinic point
prime ends

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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Cite this

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title = "Homoclinic points for convex billiards",

abstract = "In this paper we investigate some generic properties of a billiard system on a convex table. We show that C∞ generically, every hyperbolic periodic point admits some homoclinic orbit.",

keywords = "Moser stable, convex billiards, generic properties, heteroclinic connection, homoclinic point, prime ends",

author = "Zhihong Xia and Pengfei Zhang",

year = "2014",

month = jun,

doi = "10.1088/0951-7715/27/6/1181",

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T1 - Homoclinic points for convex billiards

AU - Xia, Zhihong

AU - Zhang, Pengfei

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AB - In this paper we investigate some generic properties of a billiard system on a convex table. We show that C∞ generically, every hyperbolic periodic point admits some homoclinic orbit.

KW - Moser stable

KW - convex billiards

KW - generic properties

KW - heteroclinic connection

KW - homoclinic point

KW - prime ends

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DO - 10.1088/0951-7715/27/6/1181

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SN - 0951-7715

VL - 27

SP - 1181

EP - 1192

JO - Nonlinearity

JF - Nonlinearity

IS - 6

ER -

Homoclinic points for convex billiards

Abstract

Keywords

ASJC Scopus subject areas

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