منابع مشابه
Ergodicity of Bowen-margulis Measure for the Benoist 3-manifolds: Extended Version
We study the geodesic flow of a class of 3-manifolds introduced by Benoist which have some hyperbolicity but are non-Riemannian, not CAT(0), and with non-C geodesic flow. The geometries are nonstrictly convex Hilbert geometries in dimension three which admit compact quotient manifolds by discrete groups of projective transformations. We prove the Patterson-Sullivan density is canonical, with ap...
متن کاملBowen{margulis and Patterson Measures on Negatively Curved Compact Manifolds
We give a new simple construction of the maximal entropy invariant measure (the Bowen{Margulis measure) for the geodesic ow on a compact negatively curved manifold. This construction directly connects invariant`conformal density" arising from the Patterson measure on the sphere at innnity of the universal covering space with the maximal entropy measureof the geodesic ow. 0. Introduction Let M b...
متن کاملLynn Margulis, 1938-2011.
O n November 22, 2011, Lynn Margulis, visionary biologist and tireless champion of the microbial world, died of a massive stroke. Born in 1938, Lynn was intellectually precocious, earning her bachelor’s degree from the University of Chicago at age 18 and a Berkeley PhD 6 years later. Lynn’s enduring place in science was earned soon thereafter, with the publication of her theory of endosymbiosis...
متن کاملQuantum margulis expanders
Received (received date) Revised (revised date) We present a simple way to quantize the well-known Margulis expander map. The result is a quantum expander which acts on discrete Wigner functions in the same way the classical Margulis expander acts on probability distributions. The quantum version shares all essential properties of the classical counterpart, e.g., it has the same degree and spec...
متن کاملFlat strips, Bowen-Margulis measures, and mixing of the geodesic flow for rank one CAT(0) spaces
Let X be a proper, geodesically complete CAT(0) space under a proper, non-elementary, isometric action by a group Γ with a rank one element. We construct a generalized Bowen-Margulis measure on the space of unit-speed parametrized geodesics of X modulo the Γ-action. Although the construction of Bowen-Margulis measures for rank one nonpositively curved manifolds and for CAT(−1) spaces is well-kn...
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2011
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.2407