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Homoclinic Shadowing

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Abstract

A new method for rigorously establishing the existence of a transversal homoclinic orbit to a periodic orbit (or a fixed point) of diffeomorphisms in Rn is presented. It is a computer-assisted technique with two main components. First, a global Newton’s method is devised to compute a suitable pseudo (approximate) homoclinic orbit to a pseudo periodic orbit. Then, a homoclinic shadowing theorem, which is proved herein, is invoked to establish the existence of a true transversal homoclinic orbit to a true periodic orbit near these pseudo orbits.

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Authors and Affiliations

  1. Departments of Mathematics and Computer Science, University of Miami, Coral Gables, FL, 33124, USA

    Brian A. Coomes & Hüseyin Koçak

  2. Department of Mathematics, National Taiwan University, Taipei, 106, Taiwan

    Kenneth J. Palmer

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  1. Brian A. Coomes
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  2. Hüseyin Koçak
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  3. Kenneth J. Palmer
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Correspondence to Hüseyin Koçak.

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Coomes, B.A., Koçak, H. & Palmer, K.J. Homoclinic Shadowing. J Dyn Diff Equat 17, 175–215 (2005). https://doi.org/10.1007/s10884-005-3146-x

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  • DOI: https://doi.org/10.1007/s10884-005-3146-x

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