Local Entropy Theory of a Random Dynamical System
Local Entropy Theory of a Random Dynamical System

Author: Anthony H. Dooley

Publisher: American Mathematical Soc.

Published: 2014-12-20

Total Pages: 118

ISBN-13: 1470410559

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In this paper the authors extend the notion of a continuous bundle random dynamical system to the setting where the action of R or N is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a monotone sub-additive invariant family of random continuous functions, they introduce the concept of local fiber topological pressure and establish an associated variational principle, relating it to measure-theoretic entropy. They also discuss some variants of this variational principle. The authors introduce both topological and measure-theoretic entropy tuples for continuous bundle random dynamical systems, and apply variational principles to obtain a relationship between these of entropy tuples. Finally, they give applications of these results to general topological dynamical systems, recovering and extending many recent results in local entropy theory.

Dynamical Systems Theory
Dynamical Systems Theory

Author: Jan Awrejcewicz

Publisher: BoD – Books on Demand

Published: 2020-03-25

Total Pages: 186

ISBN-13: 1838802290

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The quest to ensure perfect dynamical properties and the control of different systems is currently the goal of numerous research all over the world. The aim of this book is to provide the reader with a selection of methods in the field of mathematical modeling, simulation, and control of different dynamical systems. The chapters in this book focus on recent developments and current perspectives in this important and interesting area of mechanical engineering. We hope that readers will be attracted by the topics covered in the content, which are aimed at increasing their academic knowledge with competences related to selected new mathematical theoretical approaches and original numerical tools related to a few problems in dynamical systems theory.

Deformation Theory and Local-Global Compatibility of Langlands Correspondences
Deformation Theory and Local-Global Compatibility of Langlands Correspondences

Author: Martin Luu

Publisher: American Mathematical Soc.

Published: 2015-10-27

Total Pages: 116

ISBN-13: 1470414228

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The deformation theory of automorphic representations is used to study local properties of Galois representations associated to automorphic representations of general linear groups and symplectic groups. In some cases this allows to identify the local Galois representations with representations predicted by a local Langlands correspondence.

Locally AH-Algebras
Locally AH-Algebras

Author: Huaxin Lin

Publisher: American Mathematical Soc.

Published: 2015-04-09

Total Pages: 122

ISBN-13: 147041466X

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A unital separable -algebra, is said to be locally AH with no dimension growth if there is an integer satisfying the following: for any and any compact subset there is a unital -subalgebra, of with the form , where is a compact metric space with covering dimension no more than and is a projection, such that The authors prove that the class of unital separable simple -algebras which are locally AH with no dimension growth can be classified up to isomorphism by their Elliott invariant. As a consequence unital separable simple -algebras which are locally AH with no dimension growth are isomorphic to a unital simple AH-algebra with no dimension growth.

Recent Progress in General Topology III
Recent Progress in General Topology III

Author: K.P. Hart

Publisher: Springer Science & Business Media

Published: 2013-12-11

Total Pages: 898

ISBN-13: 946239024X

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The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland, 1992 and 2002). The book was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in 2002. The following areas experienced significant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems.

Dynamics and Numbers
Dynamics and Numbers

Author: Sergiǐ Kolyada:

Publisher: American Mathematical Soc.

Published: 2016-07-27

Total Pages: 330

ISBN-13: 1470420201

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This volume contains a collection of survey and research articles from the special program and international conference on Dynamics and Numbers held at the Max-Planck Institute for Mathematics in Bonn, Germany in 2014. The papers reflect the great diversity and depth of the interaction between number theory and dynamical systems and geometry in particular. Topics covered in this volume include symbolic dynamics, Bratelli diagrams, geometry of laminations, entropy, Nielsen theory, recurrence, topology of the moduli space of interval maps, and specification properties.

Hitting Probabilities for Nonlinear Systems of Stochastic Waves
Hitting Probabilities for Nonlinear Systems of Stochastic Waves

Author: Robert C. Dalang

Publisher: American Mathematical Soc.

Published: 2015-08-21

Total Pages: 88

ISBN-13: 1470414236

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The authors consider a d-dimensional random field u={u(t,x)} that solves a non-linear system of stochastic wave equations in spatial dimensions k∈{1,2,3}, driven by a spatially homogeneous Gaussian noise that is white in time. They mainly consider the case where the spatial covariance is given by a Riesz kernel with exponent β. Using Malliavin calculus, they establish upper and lower bounds on the probabilities that the random field visits a deterministic subset of Rd, in terms, respectively, of Hausdorff measure and Newtonian capacity of this set. The dimension that appears in the Hausdorff measure is close to optimal, and shows that when d(2−β)>2(k+1), points are polar for u. Conversely, in low dimensions d, points are not polar. There is, however, an interval in which the question of polarity of points remains open.

Higher Moments of Banach Space Valued Random Variables
Higher Moments of Banach Space Valued Random Variables

Author: Svante Janson

Publisher: American Mathematical Soc.

Published: 2015-10-27

Total Pages: 124

ISBN-13: 1470414651

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The authors define the :th moment of a Banach space valued random variable as the expectation of its :th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. The authors study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals, Pettis integrals and Dunford integrals.

Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem
Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem

Author: Jonah Blasiak

Publisher: American Mathematical Soc.

Published: 2015-04-09

Total Pages: 176

ISBN-13: 1470410117

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The Kronecker coefficient is the multiplicity of the -irreducible in the restriction of the -irreducible via the natural map , where are -vector spaces and . A fundamental open problem in algebraic combinatorics is to find a positive combinatorial formula for these coefficients. The authors construct two quantum objects for this problem, which they call the nonstandard quantum group and nonstandard Hecke algebra. They show that the nonstandard quantum group has a compact real form and its representations are completely reducible, that the nonstandard Hecke algebra is semisimple, and that they satisfy an analog of quantum Schur-Weyl duality.