Science/Engineering Ergodic Theory of Equivariant Diffeomorphisms: Markov Partitions and Stable Ergodicity (0821835998)

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Ergodic Theory of Equivariant Diffeomorphisms: Markov Partitions and Stable Ergodicity

We obtain stability and structural results for equivariant diffeomorphisms which are hyperbolic transverse to a compact (connected or finite) Lie group action and construct '$\Gamma$-regular' Markov partitions which give symbolic dynamics on the orbit space. We apply these results to the situation where $\Gamma$ is a compact connected Lie group acting smoothly on $M$ and $F$ is a smooth (at least $C^2$) $\Gamma$-equivariant diffeomorphism of $M$ such that the restriction of $F$ to the $\Gamma$- and $F$-invariant set $\Lambda\subset M$ is partially hyperbolic with left foliation given by $\Gamma$-orbits.On the assumption that the $\Gamma$-orbits all have dimension equal to that of $\Gamma$, we show that there is a naturally defined $F$- and $\Gamma$-invariant measure $\nu$ of maximal entropy on $\Lambda$ (it is not assumed that the action of $\Gamma$ is free). In this setting we prove a version of the Livsic regularity theorem and extend results of Brin on the structure of the ergodic components of compact group extensions of Anosov diffeomorphisms. We show as our main result that generically $(F,\Lambda,\nu)$ is stably ergodic (openness in the $C^2$-topology). In the case when $\Lambda$ is an attractor, we show that $\Lambda$ is generically a stably SRB attractor within the class of $\Gamma$-equivariant diffeomorphisms of $M$.

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	Science/Engineering Equivariant Stable Homotopy Theory Equivariant Stable Homotopy Theory Publisher: Springer \| ISBN: 3540168206 \| edition 1986 \| PDF \| 538 pages \| 29,64 mbOur primary purpose in this volume is to establish the foundations of equivariant stable homotopy theory. To this end, we ...
	Science/Engineering Supersymmetry and Equivariant de Rham Theory Supersymmetry and Equivariant de Rham Theory Springer \| June 11, 1999 \| ISBN-10: 354064797X \| 228 pages \| DJvu \| 2.3 mbEquivariant cohomology in the framework of smooth manifolds is the subject of this book which is part of a collection of ...
	Technical Theory of Partitions (Encyclopedia of mathematics and its applications ; v. 2 : Section, Number theory) ISBN: 0201135019 Publisher: Longman Higher Education Author: George E. AndrewsDescription:This book develops the theory of partitions. Simply put, the partitions of a number are the ways of writing that number as sums of positive integers. ...
	Mathematics Equivariant Degree Theory Jorge Ize, Alfonso Vignoli ¡°Equivariant Degree Theory" Walter de Gruyter \| 2003-06 \| ISBN: 3110175509 \| 361 pages \| PDF \| 2,1 Mb Equivariant Degree Theory (De Gruyter Series in Nonlinear Analysis and Applications,By Jorge Ize, Alfons ...
	Mathematics Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms Robert Edward Bowen ¡°Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms" Springer \| 2008-06-01 \| ISBN: 3540776052 \| 80 pages \| PDF \| 1,1 Mb For this printing of R. Bowen's book, J.-R. Chazottes has retyped it in TeX ...

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