The Experts below are selected from a list of 2058 Experts worldwide ranked by ideXlab platform

Guohua Zhang - One of the best experts on this subject based on the ideXlab platform.

  • Local variational principle concerning entropy of a sofic group action
    Journal of Functional Analysis, 2012
    Co-Authors: Guohua Zhang
    Abstract:

    Abstract Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of countable sofic groups admitting a generating measurable partition with Finite entropy; and then David Kerr and Hanfeng Li developed an operator-algebraic approach to actions of countable sofic groups not only on a standard probability space but also on a compact metric space, and established the global variational principle concerning measure-theoretic and topological entropy in this sofic context. By localizing these two kinds of entropy, in this paper we prove a local version of the global variational principle for any Finite Open Cover of the space, and show that these local measure-theoretic and topological entropies coincide with their classical counterparts when the acting group is an inFinite amenable group.

  • Local variational principle concerning entropy of a sofic group action
    arXiv: Dynamical Systems, 2011
    Co-Authors: Guohua Zhang
    Abstract:

    Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of countable sofic groups admitting a generating measurable partition with Finite entropy; and then David Kerr and Hanfeng Li developed an operator-algebraic approach to actions of countable sofic groups not only on a standard probability space but also on a compact metric space, and established the global variational principle concerning measure-theoretic and topological entropy in this sofic context. By localizing these two kinds of entropy, in this paper we prove a local version of the global variational principle for any Finite Open Cover of the space, and show that these local measure-theoretic and topological entropy coincide with their classical counterparts when the acting group is an inFinite amenable group.

  • local entropy theory for a countable discrete amenable group action
    Journal of Functional Analysis, 2011
    Co-Authors: Wen Huang, Guohua Zhang
    Abstract:

    In the paper we throw the first light on studying systematically the local entropy theory for a countable discrete amenable group action. For such an action, we introduce entropy tuples in both topological and measure-theoretic settings and build the variational relation be- tween these two kinds of entropy tuples by establishing a local variational principle for a given Finite Open Cover. Moreover, based the idea of topological entropy pairs, we introduce and study two special classes of such an action: uniformly positive entropy and completely positive entropy. Note that in the building of the local variational principle, following Romagnoli's ideas two kinds of measure-theoretic entropy are introduced for Finite Borel Covers. These two kinds of entropy turn out to be the same, where Danilenko's orbital approach becomes an inevitable tool.

Wen Huang - One of the best experts on this subject based on the ideXlab platform.

  • local entropy theory for a countable discrete amenable group action
    Journal of Functional Analysis, 2011
    Co-Authors: Wen Huang, Guohua Zhang
    Abstract:

    In the paper we throw the first light on studying systematically the local entropy theory for a countable discrete amenable group action. For such an action, we introduce entropy tuples in both topological and measure-theoretic settings and build the variational relation be- tween these two kinds of entropy tuples by establishing a local variational principle for a given Finite Open Cover. Moreover, based the idea of topological entropy pairs, we introduce and study two special classes of such an action: uniformly positive entropy and completely positive entropy. Note that in the building of the local variational principle, following Romagnoli's ideas two kinds of measure-theoretic entropy are introduced for Finite Borel Covers. These two kinds of entropy turn out to be the same, where Danilenko's orbital approach becomes an inevitable tool.

Bernard Host - One of the best experts on this subject based on the ideXlab platform.

Wei Zhaoting - One of the best experts on this subject based on the ideXlab platform.

  • Descent of dg cohesive modules for Open Covers on compact complex manifolds
    2018
    Co-Authors: Wei Zhaoting
    Abstract:

    In this paper we study the descent problem of cohesive modules on compact complex manifolds. For a complex manifold $X$ we could consider the Dolbeault dg-algebra $\mathcal{A}(X)$ on it and Block in 2006 introduced a dg-category $\mathcal{P}_{\mathcal{A}(X)}$, called cohesive modules, associated with $\mathcal{A}(X)$. The same construction works for any Open subset $U\subset X$ and we obtain a dg-presheaf on $X$ given by $U\mapsto \mathcal{P}_{\mathcal{A}(U)}$. In this paper we prove that this dg-presheaf satisfies descent for any locally Finite Open Cover of a compact manifold $X$. This generalizes a result by Ben-Bassat and Block in 2012, which studied the case that $X$ is Covered by two Open subsets.Comment: v2: minor changes. Note that this article draws heavily from a previous preprint of the author: arXiv:1605.0711

Francois Blanchard - One of the best experts on this subject based on the ideXlab platform.