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Examples of conservative diffeomorphisms of the two-dimensional torus with coexistence of elliptic and stochastic behaviour

Published online by Cambridge University Press:  19 September 2008

Feliks Przytycki
Feliks Przytycki
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, ul. Sniadeckich 8, 00-950 Warsaw, Poland
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Abstract

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We find very simple examples of C∞-arcs of diffeomorphisms of the two-dimensional torus, preserving the Lebesgue measure and having the following properties: (1) the beginning of an arc is inside the set of Anosov diffeomorphisms; (2) after the bifurcation parameter every diffeomorphism has an elliptic fixed point with the first Birkhoff invariant non-zero (the KAM situation) and an invariant open area with almost everywhere non-zero Lyapunov characteristic exponents, moreover where the diffeomorphism has Bernoulli property; (3) the arc is real-analytic except on two circles (for each value of parameter) which are inside the Bernoulli property area.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 2 , Issue 3-4 , December 1982 , pp. 439 - 463
Copyright
Copyright © Cambridge University Press 1982

References

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