99-234 J. Buzzi, G. Keller
Zeta functions and transfer operators for multidimensional piecewise affine and expanding maps (613K, postscript) Jun 17, 99
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Abstract. Let $X\subset\Bbb R^2$ be a finite union of bounded polytopes and let $T:X\to X$ be piecewise affine and eventually expanding. Then the Perron-Frobenius operator of $T$ is quasi-compact as an operator on the space of functions of bounded variation on $\Bbb R^2$ and its isolated eigenvalues (including multiplicities) are just the reciprocals of the poles of the dynamical zeta function of $T$. In higher dimensions the result remains true under an additional generically satisfied transversality assumption.

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