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Details for article 26 of 114 found articles
| Title: |
Dynamics of surface diffeomorphisms relative to homoclinic and heteroclinic orbits |
| Author: |
Collins, Pieter |
| Appeared in: |
Dynamical systems |
| Paging: | Volume 19 (2004) nr. 1 pages 1-39 |
| Year: |
2004-03 |
| Contents: |
We show how to obtain information about the dynamics of a two-dimensional discrete-time system from its homoclinic and heteroclinic orbits. The results obtained are based on the theory of 'trellises', which comprise finite-length subsets of the stable and unstable manifolds of a collection of saddle periodic orbits. For any collection of homoclinic or heteroclinic orbits, we show how to associate a canonical 'trellis type' which describes the orbits. Given a trellis type, we show how to compute a 'graph representative' which gives a combinatorial invariant of the trellis type. The orbits of the graph give the dynamics forced by the homoclinic/heteroclinic orbits in the sense that every orbit of the graph representative is 'globally shadowed' by some orbit of the system, and periodic, homoclinic/heteroclinic orbits of the graph representative are shadowed by similar orbits. |
| Publisher: |
Taylor & Francis |
| Source file: |
Elektronische Wetenschappelijke Tijdschriften |
Details for article 26 of 114 found articles
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