A maximum entropy method based on piecewise linear functions for the recovery of a stationary density of interval mappings

DOI10.1007/S10955-011-0366-9zbMath1231.37042OpenAlexW2045818727MaRDI QIDQ658511

Congming Jin, Noah H. Rhee, Aihui Zhou, Jiu Ding

Publication date: 12 January 2012

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10955-011-0366-9

zbMATH Keywords

Frobenius-Perron operatormaximum entropystationary densitypiecewise linear approximations

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Dynamical systems involving maps of the interval (37E05) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Related Items (11)

Solving Fredholm integral equations via a piecewise linear maximum entropy method ⋮ Unnamed Item ⋮ A maximum entropy method for solving the boundary value problem of second order ordinary differential equations ⋮ A Piecewise Linear Maximum Entropy Method for Invariant Measures of Random Maps with Position-Dependent Probabilities ⋮ A linear spline maximum entropy method for Frobenius-Perron operators of multi-dimensional transformations ⋮ Piecewise convex deterministic dynamical systems and weakly convex random dynamical systems and their invariant measures ⋮ Approximating solutions of Fredholm integral equations via a general spline maximum entropy method ⋮ Solving linear Volterra integral equations with a piecewise linear maximum entropy method ⋮ On Polynomial Maximum Entropy Method for Classical Moment Problem ⋮ A piecewise quadratic maximum entropy method for the statistical study of chaos ⋮ A Maximum-Entropy Meshfree Method for Computation of Invariant Measures

Cites Work

• Unnamed Item
• Finite approximation for the Frobenius-Perron operator. A solution to Ulam's conjecture
• A maximum entropy method for solving Frobenius-Perron operator equations
• Chaos, fractals, and noise: Stochastic aspects of dynamics.
• A modified piecewise linear Markov approximation of Markov operators
• Lyapunov exponents and the natural invariant density determination of chaotic maps: an iterative maximum entropy ansatz
• On the Convergence of Moment Problems
• Convergence of Best Entropy Estimates
• Maximum entropy approximation for Lyapunov exponents of chaotic maps
• Birkhoff's ergodic theorem and the piecewise-constant maximum entropy method for Frobenius–Perron operators
• A Maximum Entropy Method Based on Orthogonal Polynomials for Frobenius-Perron Operators
• Statistical Properties of Deterministic Systems

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