Absolutely continuous invariant measures for multidimensional expanding maps |
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| Authors: | Benoît Saussol |
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| Affiliation: | (1) Centre de Physique Théorique, Unité Propre de Recherche 7061, CNRS Luminy, Case 907, F-13288 Marseille-Cedex 9, France;(2) Present address: Department de Matemática, Instituto Superior Técnico, Avenida Rovisco Pais, 1049-001 Lisboa, Portugal |
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| Abstract: | We investigate the existence and statistical properties of absolutely continuous invariant measures for multidimensional expanding maps with singularities. The key point is the establishment of a spectral gap in the spectrum of the transfer operator. Our assumptions appear quite naturally for maps with singularities. We allow maps that are discontinuous on some extremely wild sets, the shape of the discontinuities being completely ignored with our approach. |
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