Is every approximate trajectory of some process near an exact trajectory of a nearby process?

DOI10.1007/BF01242136zbMath0697.58036OpenAlexW1965403106MaRDI QIDQ911123

James A. Yorke, Helena E. Nusse

Publication date: 1988

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01242136

zbMATH Keywords

chaotic dynamical systemsunimodal mapskneading sequences

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Iteration of real functions in one variable (26A18) Dynamical systems with hyperbolic behavior (37D99)

Related Items (22)

Parameter-shifted shadowing property for geometric Lorenz attractors ⋮ Using chaos to shadow the quadratic map for all time ⋮ Pathologies generated by round-off in dynamical systems ⋮ SHADOWING AND DYNAMICAL SYNTHESIS ⋮ Dynamical properties of spatial discretizations of a generic homeomorphism ⋮ Improved cost functions for modelling of noisy chaotic time series ⋮ Pseudo-orbit tracing property and structural stability of expanding maps of the interval ⋮ Cryptography with chaos and shadowing ⋮ Is every pseudo-orbit of some homeomorphism near an exact orbit of a nearby homeomorphism? ⋮ Shadowing, internal chain transitivity and \(\alpha \)-limit sets ⋮ Parameter-shifted shadowing property of Lozi maps ⋮ Expansivity and unique shadowing ⋮ NONLINEAR DYNAMICAL SYSTEM IDENTIFICATION FROM UNCERTAIN AND INDIRECT MEASUREMENTS ⋮ Numerical orbits of chaotic processes represent true orbits ⋮ Iterated maps on discretized meshes of the unit interval ⋮ Preservation of shadowing in discrete dynamical systems ⋮ On inverse shadowing ⋮ When is the beginning the end? On full trajectories, limit sets and internal chain transitivity ⋮ Shadowing for induced maps of hyperspaces ⋮ Pseudo-Orbit Shadowing in the Family of Tent Maps ⋮ Shadowing of physical trajectories in chaotic dynamics: Containment and refinement ⋮ Shadows, chaos, and saddles

Cites Work

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• On polylogarithms, Hurwitz zeta functions, and the Kubert identities
• Computing the topological entropy of maps
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• On the concept of attractor
• Qualitative analysis of the dynamics and stability properties for axiom A maps
• Sensitive dependence to initial conditions for one dimensional maps
• Randomness implies order
• Bifurcations in one dimension. I. The nonwandering set
• Small random perturbations of dynamical systems and the definition of attractors
• Universal metric properties of bifurcations of endomorphisms
• Roads to turbulence in dissipative dynamical systems
• Pseudo-Orbit Shadowing in the Family of Tent Maps
• Periodic Orbits and Kneading Invariants
• Entropy of piecewise monotone mappings
• On the Existence of Invariant Measures for Piecewise Monotonic Transformations
• Period Three Implies Chaos
• Stable Orbits and Bifurcation of Maps of the Interval
• Simple mathematical models with very complicated dynamics
• Symbolic Dynamics and Transformations of the Unit Interval

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