Normal forms with exponentially small remainder: application to homoclinic connections for the reversible \(0^{2+}i\omega\) resonance

DOI10.1016/j.crma.2004.10.002zbMath1066.34041OpenAlexW1982437849MaRDI QIDQ1764089

Eric Lombardi, Gérard Iooss

Publication date: 23 February 2005

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2004.10.002

zbMATH Keywords

normal formhomoclinic connectionexponentially small periodic orbitsreversible analytic vector fieldsresonant fixed point

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcation theory for ordinary differential equations (34C23) Periodic orbits of vector fields and flows (37C27) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

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Cites Work

• Oscillatory integrals and phenomena beyond all algebraic orders with applications to homoclinic orbits in reversible systems
• Polynomial normal forms with exponentially small remainder for analytic vector fields
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