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An estimate of entropy for toroidal chaos

Published online by Cambridge University Press:  19 September 2008

Jaroslaw Kwapisz
Jaroslaw Kwapisz
Affiliation:
Institute of Mathematics, Warsaw University, Banacha 2, Warsaw 59, Poland
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Abstract

For a mapping F:ℝ2→ℝ2 being a lift of an isotopic to the identity homeomorphism of the two-dimensional torus the rotation set ρ(F) consists of limit points of all sequences where xi, ∈ ℝ2 and ni→∞. It is known that if ρ(F) has nonempty interior then h(f) (the topological entropy of ƒ) is positive. We provide an estimate from below of h(f) in terms of ρ(F).

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 1 , March 1993 , pp. 123 - 129
Copyright
Copyright © Cambridge University Press 1993

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References

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