Shadowing and iterative interpolation for Čebyšev mixing transformations

DOI10.1016/0021-9991(92)90040-6zbMath0756.58037OpenAlexW1966773638MaRDI QIDQ1201071

D. Gavelek, Thomas Erber

Publication date: 17 January 1993

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

Full work available at URL: https://doi.org/10.1016/0021-9991(92)90040-6

zbMATH Keywords

stabilityinstabilityChebyshev polynomialsapproximationAnosov diffeomorphismsshadowingChebyshev mixing transformations

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Best approximation, Chebyshev systems (41A50) Dynamical systems with hyperbolic behavior (37D99)

Related Items

What good are numerical simulations of chaotic dynamical systems? ⋮ A model for roundoff and collapse in computation of chaotic dynamical systems ⋮ Shadowing and iterative interpolation for Čebyšev mixing transformations ⋮ Basin of attraction of cycles of discretizations of dynamical systems with SRB invariant measures.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The simulation of random processes on digital computers: Unavoidable order
• The use of Chebyshev mixing to generate pseudo-random numbers
• Do numerical orbits of chaotic dynamical processes represent true orbits?
• ACORN - A new method for generating sequences of uniformly distributed pseudo-random numbers
• Recurrence and dispersion under iteration of Cebysev polynomials
• The simulation of random processes on digital computers with Chebyshev mixing transformations
• Shadowing and iterative interpolation for Čebyšev mixing transformations
• \(\omega\)-limit sets for axiom A diffeomorphisms
• On mixing transformations
• Invariant sets under iteration of rational functions
• Stability of motion
• Mixing transformations on metric spaces
• Numerical orbits of chaotic processes represent true orbits
• The Arithmetic of the Digital Computer: A New Approach
• Pseudo-Orbit Shadowing in the Family of Tent Maps
• When is f(f(z)) = az 2 + bz + c?
• Information-Theoretic Limitations of Formal Systems
• Topological Entropy
• Ergodic and Mixing Properties of Chebyshev Polynomials