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Local and global behavior near homoclinic orbits

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Abstract

We study the local behavior of systems near homoclinic orbits to stationary points of saddle-focus type. We explicitly describe how a periodic orbit approaches homoclinicity and, with the help of numerical examples, discuss how these results relate to global patterns of bifurcations.

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Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, UK

    Paul Glendinning

  2. Department of Pure Mathematics and Mathematical Statistics, Mill Lane, Cambridge, UK

    Colin Sparrow

Authors
  1. Paul Glendinning
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  2. Colin Sparrow
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Glendinning, P., Sparrow, C. Local and global behavior near homoclinic orbits. J Stat Phys 35, 645–696 (1984). https://doi.org/10.1007/BF01010828

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