منابع مشابه
-pinched Anosov Diffeomorphism and Rigidity
Let / be a C°° Anosov diffeomorphism of a compact man-ifold M, preserving a smooth measure. If / satisfies the |-pinching assumption defined below, it must preserve a continuous affine connection for which the leaves of the Anosov foliations are totally geodesic, geodesically complete, and flat (its tangential curvature is defined along individual leaves). If this connection, which is the uniqu...
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This paper concerns pinched surfaces, also known as pseudosurfaces. A map is a graph G embedded on an oriented pinched surface. An arc of a map is an edge of G with a fixed direction. A regular map is one with a group of orientation-preserving automorphisms that acts regularly on the arcs of a map, i.e., that acts both freely and transitively. We study regular maps on pinched surfaces. We give ...
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Integer m m-matrices A with determinant 1 de ne di eomorphisms of the m-dimensional torus Tm = (IR= Z)m into itself. Likewise, they de ne bijective self-maps of the discretized tori ( Z=n Z)m = ( Zn)m. We present estimates of the surprisingly low order (or period) PerA(n) of the iteration Ar; r = 1; 2; 3; . . ., on the discretized torus ( Zn)m. We obtain PerA(n) 3n for dimension m = 2. In the s...
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We extend a number of results from one dimensional dynamics based on spectral properties of the Ruelle-Perron-Frobenius transfer operator to Anosov diffeomorphisms on compact manifolds. This allows to develop a direct operator approach to study ergodic properties of these maps. In particular, we show that it is possible to define Banach spaces on which the transfer operator is quasicompact. (In...
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We study a family of area-preserving maps of the 2-torus and show that they are pseudo-Anosov. We present a method to construct finite Markov partitions for this family which utilizes their common symmetries. Through these partitions we show explicitly that each map is a tower over a first return map, intimately linked to a toral automorphism. This enables us to calculate directly some dimensio...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1981
ISSN: 0002-9939
DOI: 10.2307/2043961