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For area preserving C2 surface diffeomorphisms, we give an explicit finite information condition on the exponential growth of the number of Bowen's (n, δ)-balls needed to cover a positive proportion… Click to show full abstract
For area preserving C2 surface diffeomorphisms, we give an explicit finite information condition on the exponential growth of the number of Bowen's (n, δ)-balls needed to cover a positive proportion of the space, that is sufficient to guarantee positive topological entropy. This can be seen as an effective version of Katok's horseshoe theorem in the conservative setting. We also show that the analogous result is false in dimension larger than 3.
Keywords:
version katok;
surface diffeomorphisms;
effective version;
horseshoe theorem;
theorem conservative;
katok horseshoe
Journal Title: Journal of Modern Dynamics
Year Published: 2017
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Journal Title: Journal of Modern Dynamics
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!