Validated numerics for equilibria of analytic vector fields: Invariant manifolds and connecting orbits

DOI10.1090/psapm/074/00642zbMath1409.65109OpenAlexW2923625401MaRDI QIDQ4557492

Jason D. Mireles James

Publication date: 23 November 2018

Published in: Rigorous Numerics in Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/psapm/074/00642

zbMATH Keywords

dynamicsnonlinear systemsordinary differential equationsinvariant manifoldshomoclinic solutionsLorenz systemglobal analysisequilibrium solutionsnumerical analysisconnecting orbitsheteroclinic solutionsTaylor methodsNewton-Kantorovichprojected boundaries

Mathematics Subject Classification ID

Invariant manifolds for ordinary differential equations (34C45) Algorithms with automatic result verification (65G20) Numerical bifurcation problems (65P30) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

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Uses Software

• RODES

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