Rigorous computations of homoclinic tangencies

Zin Arai; Konstantin Mischaikow

doi:10.1137/050626429

Rigorous computations of homoclinic tangencies

Zin Arai, Konstantin Mischaikow

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

19 Scopus citations

Abstract

In this paper, we propose a rigorous computational method for detecting homoclinic tangencies and structurally unstable connecting orbits. It is a combination of several tools and algorithms, including the interval arithmetic, the subdivision algorithm, the Conley index theory, and the computational homology theory. As an example, we prove the existence of generic homoclinic tangencies in the Henon family.

Original language	English (US)
Pages (from-to)	280-292
Number of pages	13
Journal	SIAM Journal on Applied Dynamical Systems
Volume	5
Issue number	2
DOIs	https://doi.org/10.1137/050626429
State	Published - 2006
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Modeling and Simulation

Keywords

Computational homology
Conley index
Connecting orbit
Homoclinic tangency

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10.1137/050626429

Cite this

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title = "Rigorous computations of homoclinic tangencies",

abstract = "In this paper, we propose a rigorous computational method for detecting homoclinic tangencies and structurally unstable connecting orbits. It is a combination of several tools and algorithms, including the interval arithmetic, the subdivision algorithm, the Conley index theory, and the computational homology theory. As an example, we prove the existence of generic homoclinic tangencies in the Henon family.",

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author = "Zin Arai and Konstantin Mischaikow",

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AU - Arai, Zin

AU - Mischaikow, Konstantin

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AB - In this paper, we propose a rigorous computational method for detecting homoclinic tangencies and structurally unstable connecting orbits. It is a combination of several tools and algorithms, including the interval arithmetic, the subdivision algorithm, the Conley index theory, and the computational homology theory. As an example, we prove the existence of generic homoclinic tangencies in the Henon family.

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KW - Conley index

KW - Connecting orbit

KW - Homoclinic tangency

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Rigorous computations of homoclinic tangencies

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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