The choquet simplex of invariant measures for minimal flows

1991 ◽  
Vol 74 (2-3) ◽  
pp. 241-256 ◽  
Author(s):  
Tomasz Downarowicz
Keyword(s):  
Invariant Measures ◽  
Choquet Simplex

scholarly journals Dynamical simplices and Fraïssé theory

2018 ◽  
Vol 39 (11) ◽  
pp. 3111-3126 ◽  
Author(s):  
JULIEN MELLERAY
Keyword(s):  
Invariant Measures ◽  
Probability Measures ◽  
Choquet Simplex ◽  
Cantor Space ◽  
Orbit Equivalent ◽  
Minimal Homeomorphisms

We simplify a criterion (due to Ibarlucía and the author) which characterizes dynamical simplices, that is, sets $K$ of probability measures on a Cantor space $X$ for which there exists a minimal homeomorphism of $X$ whose set of invariant measures coincides with $K$ . We then point out that this criterion is related to Fraïssé theory, and use that connection to provide a new proof of Downarowicz’ theorem stating that any non-empty metrizable Choquet simplex is affinely homeomorphic to a dynamical simplex. The construction enables us to prove that there exist minimal homeomorphisms of a Cantor space which are speedup equivalent but not orbit equivalent, answering a question of Ash.

Extending Quasi-Invariant Measures by Using Subgroups of a Given Group

2003 ◽  
Vol 10 (2) ◽  
pp. 247-255
Author(s):  
A. Kharazishvili
Keyword(s):  
Invariant Measures ◽  
Uncountable Group

Abstract A method of extending σ-finite quasi-invariant measures given on an uncountable group, by using a certain family of its subgroups, is investigated.

scholarly journals Dynamics of Systems with a Discontinuous Hysteresis Operator and Interval Translation Maps

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 80
Author(s):  
Sergey Kryzhevich ◽  
Viktor Avrutin ◽  
Nikita Begun ◽  
Dmitrii Rachinskii ◽  
Khosro Tajbakhsh
Keyword(s):  
Risk Management ◽  
Invariant Measure ◽  
Invariant Measures ◽  
Interval Exchange ◽  
Management Model ◽  
Closing Lemma ◽  
Symbolic Model ◽  
Metric Properties ◽  
Ergodic Measures ◽  
Maximal Invariant

We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and demonstrated that an ITM, endowed with such a measure, is metrically conjugated to an interval exchange map (IEM). This allowed us to extend some properties of IEMs (e.g., an estimate of the number of ergodic measures and the minimality of the symbolic model) to ITMs. Further, we proved a version of the closing lemma and studied how the invariant measures depend on the parameters of the system. These results were illustrated by a simple example or a risk management model where interval translation maps appear naturally.

Analysis of an algorithm for computing invariant measures

1995 ◽  
Vol 24 (3) ◽  
pp. 323-336 ◽  
Author(s):  
Phil Diamond ◽  
Peter Kloeden ◽  
Alexei Pokrovskii
Keyword(s):  
Invariant Measures
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