Jerome Buzzi (Ecole Polytechnique)

Quasi-finite puzzles

Abstract. Interval maps have a nice and natural symbolic dynamics. They are natural in that they are defined by their partitions into maximum interval of monotonicity. They are nice in that they are very close to subshifts of finite type. We try and generalize this to higher dimensional maps of the type:

$$(x,y) \to (1.8-x^2+0.1\sin(2\pi y),1.5-y^2+0.1\sin(2\pi x))$$

by the way of dynamical puzzles a la Yoccoz. We show that these puzzles are close to subshifts of finite type in a precise sense, which in particular implies estimates on their associated zeta functions.