Real and Complex Dynamics of a Family of Birational Maps of the Plane: The Golden Mean Subshift

We describe the (real) dynamics of a family of birational mappings of the plane. By combining complex intersection theory and techniques from smooth dynamical systems, we are able to give an essentially complete account of the behavior of both wandering and nonwandering orbits. In particular, the go...

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Bibliographic Details
Published in:American journal of mathematics 2005-06, Vol.127 (3), p.595-646
Main Authors: Bedford, Eric, Diller, Jeffrey
Format: Article
Language:English
Subjects:
Average linear density
Entropy
Exact sciences and technology
Geometry
Global analysis, analysis on manifolds
Golden mean
Homeomorphism
Laminates
Mapping
Mathematical analysis
Mathematics
Rectangles
Sciences and techniques of general use
Several complex variables and analytic spaces
Theorems
Topological manifolds
Topological theorems
Topology
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:We describe the (real) dynamics of a family of birational mappings of the plane. By combining complex intersection theory and techniques from smooth dynamical systems, we are able to give an essentially complete account of the behavior of both wandering and nonwandering orbits. In particular, the golden mean subshift provides a topological model for the dynamics on the nonwandering set. While the mappings are not hyperbolic, they are shown to possess many of the structures associated with hyperbolicity.
ISSN:0002-9327
1080-6377
1080-6377
DOI:10.1353/ajm.2005.0015