Construction of Markov Partitions in PL1D Maps

2013 ◽  
Vol 60 (10) ◽  
pp. 702-706 ◽  
Author(s):  
Toni Draganov Stojanovski ◽  
Ljupco Kocarev
Keyword(s):  
Markov Partitions

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.

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.

Markov partitions and shadowing for non-uniformly hyperbolic systems with singularities

1992 ◽  
Vol 12 (3) ◽  
pp. 487-508 ◽  
Author(s):  
Tyll Krüger ◽  
Serge Troubetzkoy
Keyword(s):  
Large Class ◽  
Hyperbolic Systems ◽  
Markov Partitions ◽  
Uniformly Hyperbolic Systems ◽  
Dispersing Billiards

AbstractWe show the existence of countable Markov partitions for a large class of non-uniformly hyperbolic systems with singularities including dispersing billiards in any dimension.

scholarly journals Schmidt games and Markov partitions

Nonlinearity ◽  
2009 ◽  
Vol 22 (3) ◽  
pp. 525-543 ◽  
Author(s):  
Jimmy Tseng
Keyword(s):  
Markov Partitions
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