John Smillie

Ergodicity of billiard flows and quadratic differentials

On considere un systeme billard de 2 objets de masses m 1 et m 2 . On montre que pour un ensemble dense de paires (m 1 ,m 2 ) ce systeme est ergodique

Polynomial diffeomorphisms of C2. IV: The measure of maximal entropy and laminar currents.

This paper concerns the dynamics of polynomial automorphisms of

Distribution of periodic points of polynomial diffeomorphisms of C2

{\bf C}^2

Polynomial diffeomorphisms of ². II. Stable manifolds and recurrence

. One can associate to such an automorphism two currents

The dynamics of Rayleigh quotient iteration

\mu^\pm

Rayleigh quotient iteration for nonsymmetric matrices

and the equilibrium measure

Polynomial diffeomorphisms of C2 : VII. Hyperbolicity and external rays

\mu=\mu^+\wedge\mu^-

Polynomial Diffeomorphisms of C 2 : VI. Connectivity of J

. In this paper we study some geometric and dynamical properties of these objects. First, we characterize

Real polynomial diffeomorphisms with maximal entropy: II. Small Jacobian

\mu

Polynomial diffeomorphisms of C 2 . VIII: Quasi-expansion

as the unique measure of maximal entropy. Then we show that the measure