Expansive foliations
Copyright policy )Expansive foliations
The authors introduce the notion of expansiveness into foliation theory. They prove that in the case of codimension-one foliations the topological structure of a foliation completely characterizes its expansiveness. It follows that the geometric entropy of a codimension-one expansive foliation is positive and that the fundamental group of a manifold admitting a codimension-one expansive foliation has exponential growth. Similar results are obtained in the case of strongly expansive foliations with arbitrary codimension.
- Chiba University Japan
- Toin University of Yokohama Japan
expansive foliation, strongly expansive foliations, Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\), Dynamical systems with hyperbolic behavior, geometric entropy, exponential growth, Foliations in differential topology; geometric theory, Ergodic theory, codimension-one foliations, fundamental group
expansive foliation, strongly expansive foliations, Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\), Dynamical systems with hyperbolic behavior, geometric entropy, exponential growth, Foliations in differential topology; geometric theory, Ergodic theory, codimension-one foliations, fundamental group
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