Local Entropy Theory Of A Random Dynamical System

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Local Entropy Theory of a Random Dynamical System

Anthony H. Dooley, Guohua Zhang
Local Entropy Theory of a Random Dynamical System Book PDF

Author : Anthony H. Dooley, Guohua Zhang
Publisher : American Mathematical Soc.
Page : 106 pages
File Size : 52,7 Mb
Release : 2014-12-20
Category : Mathematics
ISBN : 9781470410551

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Local Entropy Theory of a Random Dynamical System by Anthony H. Dooley, Guohua Zhang Pdf

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.

Smooth Ergodic Theory of Random Dynamical Systems

Pei-Dong Liu,Min Qian
Smooth Ergodic Theory of Random Dynamical Systems Book PDF

Author : Pei-Dong Liu,Min Qian
Publisher : Unknown
Page : 242 pages
File Size : 43,7 Mb
Release : 1995
Category : Mathematics
ISBN : UOM:39015049290102

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Smooth Ergodic Theory of Random Dynamical Systems by Pei-Dong Liu,Min Qian Pdf

This book studies ergodic-theoretic aspects of random dynam- ical systems, i.e. of deterministic systems with noise. It aims to present a systematic treatment of a series of recent results concerning invariant measures, entropy and Lyapunov exponents of such systems, and can be viewed as an update of Kifer's book. An entropy formula of Pesin's type occupies the central part. The introduction of relation numbers (ch.2) is original and most methods involved in the book are canonical in dynamical systems or measure theory. The book is intended for people interested in noise-perturbed dynam- ical systems, and can pave the way to further study of the subject. Reasonable knowledge of differential geometry, measure theory, ergodic theory, dynamical systems and preferably random processes is assumed.

Dynamical Systems Theory

Jan Awrejcewicz,Dariusz Grzelczyk
Dynamical Systems Theory Book PDF

Author : Jan Awrejcewicz,Dariusz Grzelczyk
Publisher : BoD – Books on Demand
Page : 186 pages
File Size : 54,7 Mb
Release : 2020-03-25
Category : Mathematics
ISBN : 9781838802295

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Dynamical Systems Theory by Jan Awrejcewicz,Dariusz Grzelczyk Pdf

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

Martin Luu
Deformation Theory and Local Global Compatibility of Langlands Correspondences Book PDF

Author : Martin Luu
Publisher : American Mathematical Soc.
Page : 101 pages
File Size : 42,8 Mb
Release : 2015-10-27
Category : Automorphic forms
ISBN : 9781470414221

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Deformation Theory and Local-Global Compatibility of Langlands Correspondences by Martin Luu Pdf

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

Huaxin Lin
Locally AH Algebras Book PDF

Author : Huaxin Lin
Publisher : American Mathematical Soc.
Page : 109 pages
File Size : 54,9 Mb
Release : 2015-04-09
Category : Mathematics
ISBN : 9781470414665

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Locally AH-Algebras by Huaxin Lin Pdf

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

K.P. Hart,J. van Mill,P. Simon
Recent Progress in General Topology III Book PDF

Author : K.P. Hart,J. van Mill,P. Simon
Publisher : Springer Science & Business Media
Page : 903 pages
File Size : 52,6 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9789462390249

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Recent Progress in General Topology III by K.P. Hart,J. van Mill,P. Simon Pdf

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.

Higher Moments of Banach Space Valued Random Variables

Svante Janson,Sten Kaijser
Higher Moments of Banach Space Valued Random Variables Book PDF

Author : Svante Janson,Sten Kaijser
Publisher : American Mathematical Soc.
Page : 110 pages
File Size : 43,6 Mb
Release : 2015-10-27
Category : Banach spaces
ISBN : 9781470414658

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Higher Moments of Banach Space Valued Random Variables by Svante Janson,Sten Kaijser Pdf

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.

Hitting Probabilities for Nonlinear Systems of Stochastic Waves

Robert C. Dalang,Marta Sanz-Solé
Hitting Probabilities for Nonlinear Systems of Stochastic Waves Book PDF

Author : Robert C. Dalang,Marta Sanz-Solé
Publisher : American Mathematical Soc.
Page : 75 pages
File Size : 53,7 Mb
Release : 2015-08-21
Category : Hausdorff measures
ISBN : 9781470414238

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Hitting Probabilities for Nonlinear Systems of Stochastic Waves by Robert C. Dalang,Marta Sanz-Solé Pdf

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.

Dynamics and Numbers

Sergiǐ Kolyada:,Martin Möller,Pieter Moree,Thomas Ward
Dynamics and Numbers Book PDF

Author : Sergiǐ Kolyada:,Martin Möller,Pieter Moree,Thomas Ward
Publisher : American Mathematical Soc.
Page : 315 pages
File Size : 53,8 Mb
Release : 2016-07-27
Category : Ergodic theory
ISBN : 9781470420208

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Dynamics and Numbers by Sergiǐ Kolyada:,Martin Möller,Pieter Moree,Thomas Ward Pdf

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.

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

Jonah Blasiak,Ketan D. Mulmuley,Milind Sohoni
Geometric Complexity Theory IV Nonstandard Quantum Group for the Kronecker Problem Book PDF

Author : Jonah Blasiak,Ketan D. Mulmuley,Milind Sohoni
Publisher : American Mathematical Soc.
Page : 160 pages
File Size : 47,8 Mb
Release : 2015-04-09
Category : Mathematics
ISBN : 9781470410117

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Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem by Jonah Blasiak,Ketan D. Mulmuley,Milind Sohoni Pdf

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.

Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients

Martin Hutzenthaler,Arnulf Jentzen
Numerical Approximations of Stochastic Differential Equations with Non Globally Lipschitz Continuous Coefficients Book PDF

Author : Martin Hutzenthaler,Arnulf Jentzen
Publisher : American Mathematical Soc.
Page : 99 pages
File Size : 43,8 Mb
Release : 2015-06-26
Category : Differential operators
ISBN : 9781470409845

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Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients by Martin Hutzenthaler,Arnulf Jentzen Pdf

Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method diverge for these SDEs in finite time. This article develops a general theory based on rare events for studying integrability properties such as moment bounds for discrete-time stochastic processes. Using this approach, the authors establish moment bounds for fully and partially drift-implicit Euler methods and for a class of new explicit approximation methods which require only a few more arithmetical operations than the Euler-Maruyama method. These moment bounds are then used to prove strong convergence of the proposed schemes. Finally, the authors illustrate their results for several SDEs from finance, physics, biology and chemistry.

On the Differential Structure of Metric Measure Spaces and Applications

Nicola Gigli
On the Differential Structure of Metric Measure Spaces and Applications Book PDF

Author : Nicola Gigli
Publisher : American Mathematical Soc.
Page : 91 pages
File Size : 53,6 Mb
Release : 2015-06-26
Category : Differential calculus
ISBN : 9781470414207

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On the Differential Structure of Metric Measure Spaces and Applications by Nicola Gigli Pdf

The main goals of this paper are: (i) To develop an abstract differential calculus on metric measure spaces by investigating the duality relations between differentials and gradients of Sobolev functions. This will be achieved without calling into play any sort of analysis in charts, our assumptions being: the metric space is complete and separable and the measure is Radon and non-negative. (ii) To employ these notions of calculus to provide, via integration by parts, a general definition of distributional Laplacian, thus giving a meaning to an expression like , where is a function and is a measure. (iii) To show that on spaces with Ricci curvature bounded from below and dimension bounded from above, the Laplacian of the distance function is always a measure and that this measure has the standard sharp comparison properties. This result requires an additional assumption on the space, which reduces to strict convexity of the norm in the case of smooth Finsler structures and is always satisfied on spaces with linear Laplacian, a situation which is analyzed in detail.

Deformation Quantization for Actions of Kahlerian Lie Groups

Pierre Bieliavsky,Victor Gayral
Deformation Quantization for Actions of Kahlerian Lie Groups Book PDF

Author : Pierre Bieliavsky,Victor Gayral
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 42,6 Mb
Release : 2015-06-26
Category : Kählerian structures
ISBN : 9781470414917

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Deformation Quantization for Actions of Kahlerian Lie Groups by Pierre Bieliavsky,Victor Gayral Pdf

Let B be a Lie group admitting a left-invariant negatively curved Kählerian structure. Consider a strongly continuous action of B on a Fréchet algebra . Denote by the associated Fréchet algebra of smooth vectors for this action. In the Abelian case BR and isometric, Marc Rieffel proved that Weyl's operator symbol composition formula (the so called Moyal product) yields a deformation through Fréchet algebra structures R on . When is a -algebra, every deformed Fréchet algebra admits a compatible pre- -structure, hence yielding a deformation theory at the level of -algebras too. In this memoir, the authors prove both analogous statements for general negatively curved Kählerian groups. The construction relies on the one hand on combining a non-Abelian version of oscillatory integral on tempered Lie groups with geom,etrical objects coming from invariant WKB-quantization of solvable symplectic symmetric spaces, and, on the second hand, in establishing a non-Abelian version of the Calderón-Vaillancourt Theorem. In particular, the authors give an oscillating kernel formula for WKB-star products on symplectic symmetric spaces that fiber over an exponential Lie group.

Level One Algebraic Cusp Forms of Classical Groups of Small Rank

Gaëtan Chenevier, David A. Renard
Level One Algebraic Cusp Forms of Classical Groups of Small Rank Book PDF

Author : Gaëtan Chenevier, David A. Renard
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 44,5 Mb
Release : 2015-08-21
Category : Cusp forms (Mathematics)
ISBN : 9781470410940

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Level One Algebraic Cusp Forms of Classical Groups of Small Rank by Gaëtan Chenevier, David A. Renard Pdf

The authors determine the number of level 1, polarized, algebraic regular, cuspidal automorphic representations of GLn over Q of any given infinitesimal character, for essentially all n≤8. For this, they compute the dimensions of spaces of level 1 automorphic forms for certain semisimple Z-forms of the compact groups SO7, SO8, SO9 (and G2) and determine Arthur's endoscopic partition of these spaces in all cases. They also give applications to the 121 even lattices of rank 25 and determinant 2 found by Borcherds, to level one self-dual automorphic representations of GLn with trivial infinitesimal character, and to vector valued Siegel modular forms of genus 3. A part of the authors' results are conditional to certain expected results in the theory of twisted endoscopy.

Multiple Hilbert Transforms Associated with Polynomials

Joonil Kim
Multiple Hilbert Transforms Associated with Polynomials Book PDF

Author : Joonil Kim
Publisher : American Mathematical Soc.
Page : 120 pages
File Size : 48,8 Mb
Release : 2015-08-21
Category : Hilbert transform
ISBN : 9781470414351

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Multiple Hilbert Transforms Associated with Polynomials by Joonil Kim Pdf

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