Abstract
We compare one-dimensional representations for the isotopy stable dynamics of homeomorphisms in two dimensions. We consider the skeleton graph representative, which captures periodic behaviour, and the homotopy graph representative which captures homo/heteroclinic behaviour. The main result of this paper is to show that the dual to the skeleton graph representative is the homotopy graph representative of the inverse map. This gives a strong link between different methods for computing the dynamics.
Original language | English |
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Pages (from-to) | 2103-2135 |
Number of pages | 33 |
Journal | Journal of Nonlinear Science |
Volume | 29 |
Issue number | 5 |
DOIs | |
Publication status | Published - Oct 2019 |
Keywords
- CHAOS
- DIFFEOMORPHISMS
- Dual graph
- Fixed-point theory
- GEOMETRY
- Homoclinic
- Homotopy lobe dynamics
- Symbolic dynamics
- TOPOLOGICAL FLUID-MECHANICS
- TRANSPORT
- Train tracks
- heteroclinic tangles