All invariant densities of piecewise linear Markov maps are piecewise constant

DOI10.1016/0196-8858(81)90008-7zbMath0468.28018OpenAlexW2022068982MaRDI QIDQ1156256

Gabriel Haddad, Boyarski, Abraham

Publication date: 1981

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0196-8858(81)90008-7

zbMATH Keywords

absolutely continuous invariant measuresdensity functions of bounded variationpiecewise linear Markov map

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Abstract differentiation theory, differentiation of set functions (28A15)

Related Items (5)

Approximating physical invariant measures of mixing dynamical systems in higher dimensions ⋮ The inverse Frobenius-Perron problem: a survey of solutions to the original problem formulation ⋮ Absolutely Continuous Invariant Measures that are Maximal ⋮ CONTROLLING CHAOS AND THE INVERSE FROBENIUS–PERRON PROBLEM: GLOBAL STABILIZATION OF ARBITRARY INVARIANT MEASURES ⋮ A manifold independent approach to understanding transport in stochastic dynamical systems

Cites Work

• Irreducibility and primitivity using Markov maps
• On a Class of Transformations which have Unique Absolutely Continuous Invariant Measures
• On the Existence of Invariant Measures for Piecewise Monotonic Transformations
• Ergodic Transformations from an Interval Into Itself

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