Geometry of slow-fast Hamiltonian systems and Painlevé equations

DOI10.1016/j.indag.2016.09.003zbMath1352.53066arXiv1511.08454OpenAlexW2963718925MaRDI QIDQ344738

Evgeniy Ivanovich Yakovlev, Lev M. Lerman

Publication date: 24 November 2016

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.08454

zbMATH Keywords

bundleHamiltonianblow-upPainlevé equationsdisruption pointpresymplectic manifoldsingular symplecticslow-fast

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Hamilton's equations (70H05)

Related Items

Geometric singular perturbation theory for systems with symmetry, On interrelations between divergence-free and Hamiltonian dynamics, Second-order fast-slow dynamics of non-ergodic Hamiltonian systems: thermodynamic interpretation and simulation, Deformations of Poisson structures on fibered manifolds and adiabatic slow–fast systems

Cites Work

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• Singularities of differentiable maps, Volume 1. Classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, edited by V. I. Arnol'd
• Periodic orbits and chaos in fast-slow systems with Bogdanov-Takens type fold points
• On singularities of mappings of Euclidean spaces. I. Mappings of the plane into the plane
• Unbounded energy growth in Hamiltonian systems with a slowly varying parameter
• The isomonodromic deformation method in the theory of Painlevé equations
• Geometric singular perturbation theory for ordinary differential equations
• Dynamical systems V. Bifurcation theory and catastrophe theory. Transl. from the Russian by N. D. Kazarinoff
• Long-periodic orbits and invariant tori in a singularly perturbed Hamiltonian system
• Painlevé equations -- nonlinear special functions.
• Slow passage through a saddle-center bifurcation
• Mixed-Mode Oscillations with Multiple Time Scales
• Slowly Varying Jump and Transition Phenomena Associated with Algebraic Bifurcation Problems
• On Coisotropic Imbeddings of Presymplectic Manifolds
• Almost invariant elliptic manifold in a singularly perturbed Hamiltonian system
• Canard cycles and center manifolds
• Averaging, passage through resonances, and capture into resonance in two-frequency systems
• Averaging methods in nonlinear dynamical systems
• Invariant manifolds