Shadows, chaos, and saddles

DOI10.1016/0168-9274(93)90141-DzbMath0784.65065WikidataQ59593915 ScholiaQ59593915MaRDI QIDQ1308574

Jesús María Sanz-Serna, Stig Larsson

Publication date: 20 December 1993

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

zbMATH Keywords

chaotic dynamicsdifference equationsdiscrete dynamical systemsshadowingbackward error analysismethod of modified equations

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Numerical investigation of stability of solutions to ordinary differential equations (65L07)

Related Items (5)

Various closeness concepts in numerical ODE's ⋮ EVALUATION OF THE COMPUTATIONAL ERRORS BY MEANS OF BIFURCATION EVENTS ⋮ Unnamed Item ⋮ Reduction of computational errors using nonstandard finite difference models ⋮ A numerical \(C^{1}\)-shadowing result for retarded functional differential equations

Cites Work

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• Aspects of backward error analysis of numerical ODEs
• Is every approximate trajectory of some process near an exact trajectory of a nearby process?
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Do numerical orbits of chaotic dynamical processes represent true orbits?
• General framework, stability and error analysis for numerical stiff boundary value methods
• \(\omega\)-limit sets for axiom A diffeomorphisms
• Numerical orbits of chaotic processes represent true orbits
• On the Numerical Approximation of Phase Portraits Near Stationary Points
• Pseudo-Orbit Shadowing in the Family of Tent Maps
• The Long-Time Behavior of Finite-Element Approximations of Solutions to Semilinear Parabolic Problems
• Rigorous verification of trajectories for the computer simulation of dynamical systems
• On the qualitative behavior of the orbits of a parabolic partial differential equation and its discretization in the neighborhood of a hyperbolic fixed point
• A note on uniform in time error estimates for approximations to reaction-diffusion equations
• The Behavior of Finite Element Solutions of Semilinear Parabolic Problems Near Stationary Points
• Shadowing of physical trajectories in chaotic dynamics: Containment and refinement
• On the Scope of the Method of Modified Equations
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms

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