Informal Remarks on the Orbit Structure of Discrete Approximations to Chaotic Maps

DOI10.1080/10586458.1998.10504377zbMath0922.58042OpenAlexW2070873916MaRDI QIDQ4235997

Oscar E. III Lanford

Publication date: 22 March 1999

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1047674149

zbMATH Keywords

orbitcomputer simulationsdiscrete mapsergodic property of maps

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Ergodic theory (37A99)

Related Items (21)

Degree of recurrence of generic diffeomorphisms ⋮ Rigorous approximation of diffusion coefficients for expanding maps ⋮ From chaos to randomness via geometric undersampling ⋮ Statistical properties of dynamical systems -- Simulation and abstract computation ⋮ Dynamical properties of spatial discretizations of a generic homeomorphism ⋮ COARSE-GRAINED OBSERVATION OF DISCRETIZED MAPS ⋮ Cramér distance and discretisations of circle expanding maps I: theory ⋮ Cramér distance and discretizations of circle expanding maps II: simulations ⋮ Accurate bounds on Lyapunov exponents for expanding maps of the interval ⋮ Adaptive cellular integration of linearly implicit differential equations ⋮ An elementary way to rigorously estimate convergence to equilibrium and escape rates ⋮ Rigorous computation of diffusion coefficients for expanding maps ⋮ Optimal linear responses for Markov chains and stochastically perturbed dynamical systems ⋮ Probability, statistics and computation in dynamical systems ⋮ Cryptography-Based Chaos via Geometric Undersampling of Ring-Coupled Attractors ⋮ The Challenging Problem of Industrial Applications of Multicore-Generated Iterates of Nonlinear Mappings ⋮ Towards understanding the theoretical challenges of numerical modeling of dynamical systems ⋮ BRANCHING PROCESSES AND COMPUTATIONAL COLLAPSE OF DISCRETIZED UNIMODAL MAPPINGS ⋮ EMERGENCE OF RANDOMNESS FROM CHAOS ⋮ Sturdy cycles in the chaotic ``Tribolium castaneum data series ⋮ Numerical coalescence of chaotic trajectories

Cites Work

• The simulation of random processes on digital computers: Unavoidable order
• The simulation of random processes on digital computers with Chebyshev mixing transformations
• Basin of attraction of cycles of discretizations of dynamical systems with SRB invariant measures.

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