How to compute the Melnikov vector ?

Alaan Goriely; Michael Tabor

doi:10.1145/190347.190418

How to compute the Melnikov vector ?

Alaan Goriely, Michael Tabor

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

It is shown that transverse homoclinic intersections such as the ones described by the Melnikov theory can be computed by a local analysis of the complex-Time singularities of the solutions. This provides a new algorithmic procedure to compute homoclinic intersections in n-dimensions once the homoclinic manifold is known. It also gives new insights on the singularity structure of integrable and nonintegrable systems.

Original language	English (US)
Title of host publication	Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC 1994
Publisher	Association for Computing Machinery
Pages	205-210
Number of pages	6
ISBN (Electronic)	0897916387
DOIs	https://doi.org/10.1145/190347.190418
State	Published - Aug 1 1994
Externally published	Yes
Event	1994 International Symposium on Symbolic and Algebraic Computation, ISSAC 1994 - Oxford, United Kingdom Duration: Jul 20 1994 → Jul 22 1994

Publication series

Name	Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC
Volume	Part F129423

Other

Other	1994 International Symposium on Symbolic and Algebraic Computation, ISSAC 1994
Country/Territory	United Kingdom
City	Oxford
Period	7/20/94 → 7/22/94

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1145/190347.190418

Cite this

How to compute the Melnikov vector ? / Goriely, Alaan; Tabor, Michael.
Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC 1994. Association for Computing Machinery, 1994. p. 205-210 (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC; Vol. Part F129423).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Goriely, A & Tabor, M 1994, How to compute the Melnikov vector ? in Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC 1994. Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, vol. Part F129423, Association for Computing Machinery, pp. 205-210, 1994 International Symposium on Symbolic and Algebraic Computation, ISSAC 1994, Oxford, United Kingdom, 7/20/94. https://doi.org/10.1145/190347.190418

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title = "How to compute the Melnikov vector ?",

abstract = "It is shown that transverse homoclinic intersections such as the ones described by the Melnikov theory can be computed by a local analysis of the complex-Time singularities of the solutions. This provides a new algorithmic procedure to compute homoclinic intersections in n-dimensions once the homoclinic manifold is known. It also gives new insights on the singularity structure of integrable and nonintegrable systems.",

author = "Alaan Goriely and Michael Tabor",

note = "Publisher Copyright: {\textcopyright} 1994 ACM.; 1994 International Symposium on Symbolic and Algebraic Computation, ISSAC 1994 ; Conference date: 20-07-1994 Through 22-07-1994",

year = "1994",

month = aug,

day = "1",

doi = "10.1145/190347.190418",

language = "English (US)",

series = "Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC",

publisher = "Association for Computing Machinery",

pages = "205--210",

booktitle = "Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC 1994",