Simultaneous dense and non-dense orbits for toral diffeomorphisms
Tseng, J
Date: 1 June 2017
Journal
Ergodic Theory and Dynamical Systems
Publisher
Cambridge University Press
Publisher DOI
Abstract
We show that, for pairs of hyperbolic toral automorphisms on the -torus, the points with dense forward orbits under one map and non-dense forward orbits under the other is a dense, uncountable set. The pair of maps can be non-commuting. We also show the same for pairs of -Anosov diffeomorphisms on the -torus. (The pairs must ...
We show that, for pairs of hyperbolic toral automorphisms on the -torus, the points with dense forward orbits under one map and non-dense forward orbits under the other is a dense, uncountable set. The pair of maps can be non-commuting. We also show the same for pairs of -Anosov diffeomorphisms on the -torus. (The pairs must satisfy slight constraints.) Our main tools are the Baire category theorem and a geometric construction that allows us to give a geometric characterization of the fractal that is the set of points with forward orbits that miss a certain open set.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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