Rigorous and accurate enclosure of invariant manifolds on surfaces

DOI10.1134/S1560354710020024zbMath1203.37030OpenAlexW2029331869MaRDI QIDQ618187

J. Grote, Martin Berz, Kyoko Makino, Sheldon E. Newhouse, Alexander Wittig

Publication date: 14 January 2011

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1560354710020024

zbMATH Keywords

Taylor modelhyperbolicityinvariant manifoldhomoclinic point

Mathematics Subject Classification ID

Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

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Uses Software

• Cosy

Cites Work

• Stable and unstable manifolds of the Henon mapping
• Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models
• Taylor models and floating-point arithmetic: proof that arithmetic operations are validated in COSY
• The parameterization method for invariant manifolds I: Manifolds associated to non-resonant subspaces
• The parameterization method for invariant manifolds II: regularity with respect to parameters
• Tangencies for Real and Complex Hénon Maps: An Analytic Method
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