Geometrical approach to the splitting of separatrix for standard-like mappings

DOI10.1016/S0375-9601(00)00813-6zbMath0972.37029OpenAlexW1986058006MaRDI QIDQ1595783

Kiyotaka Tanikawa, Yoshihiro Yamaguchi

Publication date: 13 February 2001

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0375-9601(00)00813-6

zbMATH Keywords

manifoldsfunctional dependencecritical tangent bifurcation parameter

Mathematics Subject Classification ID

Bifurcations of singular points in dynamical systems (37G10)

Related Items

Heteroclinic bifurcations and chaotic transport in the two-harmonic standard map

Cites Work

• On integrable mappings of standard type
• Heteroclinic orbits and flux in a perturbed integrable Suris map
• A proof of the exponentially small transversality of the separatrices for the standard map
• Splitting of separatrices for standard and semistandard mappings
• Existence of exponentially small separatrix splittings and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems
• Transcendentally small transversality in the rapidly forced pendulum
• Exponentially small splitting of separatrices, matching in the complex plane and Borel summation
• Saddle connections and heteroclinic orbits for standard maps
• Asymptotic expansion of homoclinic structures in a symplectic mapping

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