Stationary policies with Markov partition property

2010 ◽  
Vol 13 (6) ◽  
pp. 1323-1341 ◽  
Author(s):  
John E. Goulionis ◽  
Dimitrios I. Stengos ◽  
George Tzavelas
Keyword(s):  
Markov Partition ◽  
Partition Property

scholarly journals Symbolic dynamics for non-uniformly hyperbolic systems

2020 ◽  
pp. 1-68
Author(s):  
YURI LIMA
Keyword(s):  
Symbolic Dynamics ◽  
Hyperbolic Systems ◽  
Markov Partition ◽  
Equilibrium Measures ◽  
Markov Partitions ◽  
Recent Advances ◽  
Closed Orbits ◽  
Symbolic Extension ◽  
Uniformly Hyperbolic Systems

Abstract This survey describes the recent advances in the construction of Markov partitions for non-uniformly hyperbolic systems. One important feature of this development comes from a finer theory of non-uniformly hyperbolic systems, which we also describe. The Markov partition defines a symbolic extension that is finite-to-one and onto a non-uniformly hyperbolic locus, and this provides dynamical and statistical consequences such as estimates on the number of closed orbits and properties of equilibrium measures. The class of systems includes diffeomorphisms, flows, and maps with singularities.

The construction of a quantum Markov partition

1999 ◽  
Vol 32 (42) ◽  
pp. 7273-7286 ◽  
Author(s):  
Raúl O Vallejos ◽  
Marcos Saraceno
Keyword(s):  
Markov Partition

Effects of the Pore Partition Property on the Drum Strength of Coke.

1994 ◽  
Vol 73 (12) ◽  
pp. 1060-1067 ◽  
Author(s):  
Shingo ASADA ◽  
Masaru NISHIMURA ◽  
Yutaka NOJIMA
Keyword(s):  
Partition Property

A combinatorial property of pκλ

1976 ◽  
Vol 41 (1) ◽  
pp. 225-234
Author(s):  
Telis K. Menas
Keyword(s):  
Large Cardinals ◽  
Combinatorial Property ◽  
Combinatorial Properties ◽  
Partition Property ◽  
Homogeneous Set ◽  
Unbounded Subset

In a paper on combinatorial properties and large cardinals [2], Jech extended several combinatorial properties of a cardinal κ to analogous properties of the set of all subsets of λ of cardinality less than κ, denoted by “pκλ”, where λ is any cardinal ≤κ. We shall consider in this paper one of these properties which is historically rooted in a theorem of Ramsey [10] and in work of Rowbottom [12].As in [2], define [pκλ]2 = {{x, y}: x, y ∈ pκλ and x ≠ y}. An unbounded subset A of pκλ is homogeneous for a function F: [pκλ]2 → 2 if there is a k < 2 so that for all x, y ∈ A with either x ⊊ y or y ⊊ x, F({x, y}) = k. A two-valued measure ü on pκλ is fine if it is κ-complete and if for all α < λ, ü({x ∈ pκλ: α ∈ x}) = 1, and ü is normal if, in addition, for every function f: pκλ → λsuch that ü({x ∈ pκλ: f(x) ∈ x}) = 1, there is an α < λ such that ü({x ∈ pκλ: f(x) = α}) = 1. Finally, a fine measure on pκλ has the partition property if every F: [pκλ]2 → 2 has a homogeneous set of measure one.

scholarly journals On the partition property of measures onPℋλ

1982 ◽  
Vol 5 (4) ◽  
pp. 817-821
Author(s):  
Donald H. Pelletier
Keyword(s):  
Measurable Cardinal ◽  
Combinatorial Property ◽  
Partition Property ◽  
Normal Measure

The partition property for measures onPℋλwas formulated by analogy with a property which Rowbottom [1] proved was possessed by every normal measure on a measurable cardinal. This property has been studied in [2], [3], and [4]. This note summarizes [5] and [6], which contain results relating the partition property with the extendibility of the measure and with an auxiliary combinatorial property introduced by Menas in [4]. Detailed proofs will appear in [5] and [6].

scholarly journals Markov partition for dispersed billiards

1986 ◽  
Vol 107 (2) ◽  
pp. 357-358 ◽  
Author(s):  
L. A. Bunimovich ◽  
Ya. G. Sinai
Keyword(s):  
Markov Partition

scholarly journals Generating special Markov partitions for hyperbolic toral automorphisms using fractals

1986 ◽  
Vol 6 (3) ◽  
pp. 325-333 ◽  
Author(s):  
Tim Bedford
Keyword(s):  
Transition Matrix ◽  
Markov Partition ◽  
Natural Conditions ◽  
Markov Partitions ◽  
Toral Automorphisms

AbstractWe show that given some natural conditions on a 3 × 3 hyperbolic matrix of integers A(det A = 1) there exists a Markov partition for the induced map A(x + ℤ3) = A(x)+ℤ3 on T3 whose transition matrix is (A−1)t. For expanding endomorphisms of T2 we construct a Markov partition so that there is a semiconjugacy from a full (one-sided) shift.

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