Quasi-periodic bifurcations in reversible systems

DOI10.1134/S1560354710520059zbMath1225.37059MaRDI QIDQ2430535

Heinz Hanßmann

Publication date: 7 April 2011

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

zbMATH Keywords

persistenceKAM theoryinvariant toriversal unfolding

Mathematics Subject Classification ID

Quasi-periodic motions and invariant tori for nonlinear problems in mechanics (70K43) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Infinite nonwandering sets arising in bifurcations of dynamical systems (37G30)

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Whitney smooth families of invariant tori within the reversible context 2 of KAM theory ⋮ A new KAM theorem for the hyperbolic lower dimensional tori in reversible systems ⋮ On the persistence of degenerate lower-dimensional tori in reversible systems ⋮ Non-Floquet invariant tori in reversible systems ⋮ Response solutions for degenerate reversible harmonic oscillators with zero-average perturbation ⋮ Quasi-periodic perturbations within the reversible context 2 in KAM theory ⋮ Non-degeneracy conditions in KAM theory ⋮ Degenerate lower dimensional tori in reversible systems ⋮ Persistence of degenerate lower dimensional invariant tori in reversible systems with Bruno non-degeneracy conditions ⋮ A KAM theorem for the elliptic lower dimensional tori with one normal frequency in reversible systems ⋮ On the persistence of lower-dimensional tori in reversible systems with high dimensional degenerate equilibrium under small perturbations ⋮ Completely degenerate lower-dimensional invariant tori in reversible systems ⋮ On the persistence of lower-dimensional elliptic tori with prescribed frequencies in reversible systems

Cites Work

• Unnamed Item
• A parametrised version of Moser's modifying terms theorem
• Local and semi-local bifurcations in Hamiltonian dynamical systems. Results and examples
• Normal linear stability of quasi-periodic tori
• Time-reversal symmetry in dynamical systems: a survey
• The reversible umbilic bifurcation
• Quasi-periodic stability of normally resonant tori
• Reversible systems
• The quasi-periodic centre-saddle bifurcation
• A KAM theorem for hyperbolic-type degenerate lower dimensional tori in Hamiltonian systems
• Local bifurcations on the plane with reversing point group symmetry
• Unfoldings of quasi-periodic tori in reversible systems
• Singularities of reversible vector fields
• Invariant tori in non-degenerate nearly integrable Hamiltonian systems
• Persistence properties of normally hyperbolic Tori
• KAM à la R
• The reversible context 2 in KAM theory: the first steps
• Convergent series expansions for quasi-periodic motions
• Quasi-periodic motions in families of dynamical systems. Order amidst chaos
• A proof of the isoenergetic KAM-theorem from the ``ordinary one
• THE QUASI-PERIODIC REVERSIBLE HOPF BIFURCATION
• Quasi-periodic solutions and stability of the equilibrium for quasi-periodically forced planar reversible and Hamiltonian systems under the Bruno condition
• Normal-internal resonances in quasi-periodically forced oscillators: a conservative approach
• The iteration-approximation decoupling in the reversible KAM theory
• Normal Form of Reversible Systems and Persistence of Lower Dimensional Tori under Weaker Nonresonance Conditions
• On the Destruction of Resonant Lagrangean Tori in Hamiltonian Systems
• Unfoldings and bifurcations of quasi-periodic tori
• Invariant manifolds