Besicovitch Covering Lemma, Hadamard manifolds, and zero entropy

1991 ◽  
Vol 1 (4) ◽  
pp. 373-382
Author(s):  
Quo-Shin Chi
Keyword(s):  
Hadamard Manifolds ◽  
Covering Lemma ◽  
Zero Entropy ◽  
Besicovitch Covering Lemma

The Besicovitch covering lemma and maximal functions

2019 ◽  
Vol 49 (2) ◽  
pp. 539-555
Author(s):  
Steven G. Krantz
Keyword(s):  
Maximal Functions ◽  
Covering Lemma ◽  
Besicovitch Covering Lemma

A ratio ergodic theorem for Borel actions of ℤd×ℝk

2012 ◽  
Vol 32 (2) ◽  
pp. 675-689
Author(s):  
ERIC HOLT
Keyword(s):  
Ergodic Theorem ◽  
Measure Space ◽  
Main Tool ◽  
Finite Measure ◽  
Covering Lemma ◽  
Finite Measure Space ◽  
Besicovitch Covering Lemma ◽  
Ratio Ergodic Theorem

AbstractWe prove a ratio ergodic theorem for free Borel actions of ℤd×ℝk on a standard Borel σ-finite measure space. The proof employs a lemma by Hochman involving coarse dimension, as well as the Besicovitch covering lemma. Due to possible singularity of the measure, we cannot use functional analytic arguments and therefore use Rudolph’s diffusion of the measure onto the orbits of the action. This diffused measure is denoted μx, and our averages are of the form (1/(μx(Bn)))∫ Bnf∘T−v(x) dμx(v). A Følner condition on the orbits of the action is shown, which is the main tool used in the proof of the ergodic theorem.

scholarly journals Common Solution for a Finite Family of Equilibrium Problems, Quasi-Variational Inclusion Problems and Fixed Points on Hadamard Manifolds

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1161
Author(s):  
Jinhua Zhu ◽  
Jinfang Tang ◽  
Shih-sen Chang ◽  
Min Liu ◽  
Liangcai Zhao
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Finite Family ◽  
Variational Inclusion ◽  
Point Problem ◽  
Hadamard Manifolds ◽  
Inclusion Problems ◽  
Common Solution

In this paper, we introduce an iterative algorithm for finding a common solution of a finite family of the equilibrium problems, quasi-variational inclusion problems and fixed point problem on Hadamard manifolds. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in literature.

Splitting Algorithms for Equilibrium Problems and Inclusion Problems on Hadamard Manifolds

2021 ◽  
pp. 1-38
Author(s):  
Konrawut Khammahawong ◽  
Poom Kumam ◽  
Parin Chaipunya
Keyword(s):  
Equilibrium Problems ◽  
Hadamard Manifolds ◽  
Inclusion Problems ◽  
Splitting Algorithms

A New Algorithm for Monotone Inclusion Problems and Fixed Points on Hadamard Manifolds with Applications

2021 ◽  
Vol 41 (4) ◽  
pp. 1250-1262
Author(s):  
Shih-sen Chang ◽  
Jinfang Tang ◽  
Chingfeng Wen
Keyword(s):  
Fixed Points ◽  
Hadamard Manifolds ◽  
Monotone Inclusion ◽  
Inclusion Problems

Variational inequalities on Hadamard manifolds

2003 ◽  
Vol 52 (5) ◽  
pp. 1491-1498 ◽  
Author(s):  
S.Z. Németh
Keyword(s):  
Variational Inequalities ◽  
Hadamard Manifolds

On the metric projection onto φ-convex subsets of Hadamard manifolds

2011 ◽  
Vol 26 (2) ◽  
pp. 815-826 ◽  
Author(s):  
A. Barani ◽  
S. Hosseini ◽  
M. R. Pouryayevali
Keyword(s):  
Metric Projection ◽  
Hadamard Manifolds ◽  
Convex Subsets

scholarly journals A topological lens for a measure-preserving system

2010 ◽  
Vol 31 (1) ◽  
pp. 49-75 ◽  
Author(s):  
E. GLASNER ◽  
M. LEMAŃCZYK ◽  
B. WEISS
Keyword(s):  
Topological Entropy ◽  
Periodic Points ◽  
Positive Entropy ◽  
Topological Properties ◽  
Topologically Transitive ◽  
Topological System ◽  
Zero Entropy ◽  
Weakly Mixing ◽  
Dynamical Properties

AbstractWe introduce a functor which associates to every measure-preserving system (X,ℬ,μ,T) a topological system $(C_2(\mu ),\tilde {T})$ defined on the space of twofold couplings of μ, called the topological lens of T. We show that often the topological lens ‘magnifies’ the basic measure dynamical properties of T in terms of the corresponding topological properties of $\tilde {T}$. Some of our main results are as follows: (i) T is weakly mixing if and only if $\tilde {T}$ is topologically transitive (if and only if it is topologically weakly mixing); (ii) T has zero entropy if and only if $\tilde {T}$ has zero topological entropy, and T has positive entropy if and only if $\tilde {T}$ has infinite topological entropy; (iii) for T a K-system, the topological lens is a P-system (i.e. it is topologically transitive and the set of periodic points is dense; such systems are also called chaotic in the sense of Devaney).

Zero-entropy vertex maps on graphs

2009 ◽  
Vol 15 (1) ◽  
pp. 17-22
Author(s):  
Chris Bernhardt
Keyword(s):  
Zero Entropy
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