Examples of conservative diffeomorphisms of the two-dimensional torus with coexistence of elliptic and stochastic behaviour
- 1 December 1982
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 2 (3-4) , 439-463
- https://doi.org/10.1017/s0143385700001711
Abstract
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.Keywords
This publication has 1 reference indexed in Scilit:
- CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORYRussian Mathematical Surveys, 1977