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Mean Ergodic Weighted Shifts on Köthe Echelon Spaces
Necessary and sufficient conditions are given for mean ergodicity, power boundedness, and topologizability for weighted backward shift and weighted...
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Ergodic Dynamics From Basic Theory to Applications
This textbook provides a broad introduction to the fields of dynamical systems and ergodic theory. Motivated by examples throughout, the author...
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Exterior Dirichlet and Neumann Problems and the Linked Ergodic Inverse Problems in the Entire Space
The paper is mainly concerned with the interconnection of the boundary behaviour of the solutions of the exterior Dirichlet and Neumann problems of...
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On Stability of Discrete Dynamical Systems: From Global Methods to Ergodic Theory Approaches
The aim of this paper is to give a complete description of the input–output methods for uniform exponential stability of discrete dynamical systems....
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The True Story of Quantum Ergodic Theorem
Let M be a smooth compact Riemannian manifold, and $$\Delta...
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Basic Ergodic Theory
These notes are based on the course of six lectures given by the first named author at the well-run workshop organised at IIT-Delhi in the month of...
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Ergodic Theorems
There are many theorems that are referred to as ergodic theorems and we present a few of the classical theorems in this chapter. For simplicity of...
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A Mean Ergodic Theorem for Nonexpansive Map**s in Hadamard Spaces
In this paper, we prove a mean ergodic theorem for nonexpansive map**s in Hadamard (nonpositive curvature complete metric) spaces, which extends...
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On the bounded cohomology for ergodic nonsingular actions of amenable groups
Let Γ be an amenable countable discrete group. Fix an ergodic free non-singular action of Γ on a nonatomic standard probability space. Let G be a...
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The Maximum Pointwise Rate of Convergence in Birkhoff’s Ergodic Theorem
A criterion for the maximum possible pointwise convergence rate in Birkhoff’s ergodic theorem for ergodic semiflows in a Lebesgue space is obtained....
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The History of V. A. Rokhlin’s Ergodic Seminar (1960–1970)
The paper tells about the main features and events of the ergodic seminar organized and headed by V. A. Rokhlin at the Leningrad State University....
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Harris Ergodic Theorem
The chapter starts with a simple version of the Harris ergodic theorem where the entire state space is a petite set. Under this hypothesis, the law...
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Ergodic Theory
Laws of large numbers, e.g., for i.i.d. random variables X 1, X 2, …, state that the sequence of averages converges a.s. to the expected value,...
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Spectral Theory, Stability and Continuation
In the framework of nonautonomous difference equations, we review tools to describe stability and hyperbolicity based on their linearisation, namely...
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Ergodic Properties of Markov Processes
Transition and contraction operators, operator ergodic theorem, maximum inequalities, ratio ergodic theorem, filling operators and functionals, ratio...
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The Generalized Entropy Ergodic Theorem for Nonhomogeneous Bifurcating Markov Chains Indexed by a Binary Tree
In this paper, we study the generalized entropy ergodic theorem for nonhomogeneous bifurcating Markov chains indexed by a binary tree. Firstly, by...
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Statistical Solutions, Ergodic Hypothesis, and Turbulence
We conclude our discussion concerning qualitative properties of weak solutions to the Navier–Stokes–Fourier system by develo** the theory of...