99-443 J. Buzzi & V. Maume-Deschamps
Decay of correlations for piecewise invertible maps in higher dimensions (741K, POSTSCRIPT) Nov 24, 99
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Abstract. We study the mixing properties of equilibrium states $\mu$ of non-Markov piecewise invertible maps $T:X\to X$, especially in the multidimensional case. Assuming mainly H\"older continuity and that the topological pressure of the boundary is smaller than the total topological pressure, we establish exponential decay of correlations, i.e.: $$\left| \int_X \varphi\cdot\psi\circ T^n\, d\mu - \int_X \varphi\,d\mu\cdot\int_X \psi\,d\mu \right| \leq C \cdot e^{-\alpha n}$$ for all H\"older functions $\varphi,\psi:X\to\Bbb R$, all $n\geq0$ and some $C<\infty$, $\alpha>0$. If the smoothness assumption is further weakened, we get subexponential speeds.

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