Sections of Hamiltonian systems

DOI10.1134/S156035472104002XzbMath1490.37084arXiv2012.10169OpenAlexW3116768634WikidataQ114074879 ScholiaQ114074879MaRDI QIDQ2058520

Konstantinos Kourliouros

Publication date: 9 December 2021

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

Full work available at URL: https://arxiv.org/abs/2012.10169

zbMATH Keywords

singularitiesHamiltonian systemsnormal formsconstraintsfunctional moduli

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Constrained dynamics, Dirac's theory of constraints (70H45) Singularities of differentiable mappings in differential topology (57R45) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15) General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants (37J06) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

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
• Singularities in variational calculus
• Le lemme de Morse isochore
• Equivalence of glancing hypersurfaces. II
• Lagrangian manifolds with singularities, asymptotic rays, and the open swallowtail
• Sur le lemme de Morse
• Equivalence of glancing hyper-surfaces
• Les variétés de Poisson et leurs algèbres de Lie associees
• Morse-Darboux lemma for surfaces with boundary
• An isochore versal deformation theorem
• Convergence versus integrability in Birkhoff normal form
• Local diffeomorphisms in symplectic space and Hamiltonian systems with constraints
• Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.
• Gauss-Manin connections for boundary singularities and isochore deformations
• CRITICAL POINTS OF FUNCTIONS ON A MANIFOLD WITH BOUNDARY, THE SIMPLE LIE GROUPSB_k,C_k, ANDF₄AND SINGULARITIES OF EVOLUTES
• Singularities of systems of rays
• Generalized Hamiltonian Dynamics
• Dynamical systems. IV. Symplectic geometry and its applications. Transl. from the Russian by G. Wassermann.

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