- 99-234 J. Buzzi, G. Keller
- Zeta functions and transfer operators for multidimensional piecewise affine
and expanding maps
Jun 17, 99
(auto. generated ps),
of related papers
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.