Conditional Stability and Real Analytic Pseudo-Anosov Maps

Marlies Gerber

1985 թ. հնվ · American Mathematical Society: Memoirs of the American Mathematical Society Գիրք 321 · American Mathematical Soc.

Այս էլ․ գրքի մասին

We show that the smooth pseudo-Anosov diffeomorphisms constructed by Gerber and Katok satisfy a "conditional structural stability" property, i.e. structural stability with respect to C1 perturbations which preserve some finite number of jets at a given finite collection of points.As a corollary, we obtain real analytic diffeomorphisms which are Bernoulli with respect to a smooth invariant measure and which are conjugate to Thurston's pseudo-Anosov homeomorphisms. These results also hold for generalized pseudo-Anosov diffeomorphisms. In particular, this proves the existence of real-analytic Bernoulli diffeomorphisms on the two-dimensional disk which preserve Lebesgue measure.