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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.

Real and complex dynamics of a family of birational maps of the plane: The golden mean subshift