Absolutely continuous invariant measure of a piecewise concave mapping of [0, 1]

DOI10.1016/S0362-546X(97)82864-7zbMath0868.47006OpenAlexW2037716728MaRDI QIDQ5284502

Jiu Ding

Publication date: 23 February 1997

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0362-546x(97)82864-7

zbMATH Keywords

Frobenius-Perron operatorMarkov finite approximationunique normalized absolute continuous invariant measure

Mathematics Subject Classification ID

Classes of sets (Borel fields, (sigma)-rings, etc.), measurable sets, Suslin sets, analytic sets (28A05) Ergodic theory of linear operators (47A35) Linear operators on function spaces (general) (47B38)

Related Items (4)

Computing fixed densities of a class of Frobenius-Perron operators ⋮ The asymptotic behavior of Frobenius-Perron operator with local lower-bound function ⋮ Rank ordered beta distributions of nonlinear map symbolic dynamics families with a first-order transition between dynamical regimes ⋮ Weakly Convex and Concave Random Maps with Position Dependent Probabilities

Cites Work

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• Absolutely continuous invariant measures for one-parameter families of one-dimensional maps
• On the approximation of invariant measures
• Finite approximation for the Frobenius-Perron operator. A solution to Ulam's conjecture
• A finite element method for the Frobenius-Perron operator equation
• Chaos, fractals, and noise: Stochastic aspects of dynamics.
• Computing invariant measures of piecewise convex transformations.
• Exact Dynamical Systems and the Frobenius-Perron Operator
• Markov finite approximation of Frobenius-Perron operator
• Error estimates of the Markov finite approximation of the Frobenius-Perron operator
• On the Existence of Invariant Measures for Piecewise Monotonic Transformations
• Stability and approximation of invariant measures for a class of nonexpanding transformations

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