BIFURCATION CURVES OF SUBHARMONIC SOLUTIONS AND MELNIKOV THEORY UNDER DEGENERACIES
DOI10.1142/S0129055X07002985zbMath1202.34078arXivmath/0604098MaRDI QIDQ3444901
Michele V. Bartuccelli, Jonathan H. B. Deane, Guido Gentile
Publication date: 5 June 2007
Published in: Reviews in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0604098
perturbation theorydegeneracydissipative systemsubharmonic solutionbifurcation curvediagrammatic rulessubharmonic Melnikov functionforced systemtree formalism
Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Perturbations of ordinary differential equations (34D10) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Bifurcations connected with nontransversal intersection in dynamical systems (37G25)
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Cites Work
- A note on a generalization of Françoise's algorithm for calculating higher order Melnikov functions
- Stability for quasi-periodically perturbed Hill's equations
- Globally and locally attractive solutions for quasi-periodically forced systems
- Borel summability and Lindstedt series
- Pure point spectrum for two-level systems in a strong quasi-periodic field
- The successive derivatives of the period function of a plane vector field
- Higher order bifurcations of limit cycles
- Lower dimensional invariant tori in the regions of instability for nearly integrable Hamiltonian systems
- Scaling properties for the radius of convergence of a Lindstedt series: The standard map
- Twistless KAM tori
- Quasi-periodic solutions for two-level systems
- Scaling properties for the radius of convergence of Lindstedt series: Generalized standard maps
- Resonance tongues in Hill's equations: A geometric approach
- Global attraction to the origin in a parametrically driven nonlinear oscillator
- A generalization of Françoise's algorithm for calculating higher order Melnikov functions
- Hyperbolic low-dimensional invariant tori and summations of divergent series
- Geometrical aspects of stability theory for Hill's equations
- Birkhoff-Kolmogorov-Arnold-Moser tori in convex Hamiltonian systems
- Subharmonic solutions of second order equations arising near harmonic solutions
- Higher-order Melnikov functions for single-DOF mechanical oscillators: theoretical treatment and applications
- Degenerate elliptic resonances
- Degenerate lower-dimensional tori under the Bryuno condition
- Summation of divergent series and Borel summability for strongly dissipative differential equations with periodic or quasiperiodic forcing terms
- Fractional Lindstedt series
- Quasiperiodic attractors, Borel summability and the Bryuno condition for strongly dissipative systems
- Invariant sets for the varactor equation
- Bifurcation near degenerate families
- Interaction of damping and forcing in a second order equation
- Formal integrals for an autonomous Hamiltonian system near an equilibrium point
- A theory for imperfect bifurcation via singularity theory
- LINDSTEDT SERIES FOR PERTURBATIONS OF ISOCHRONOUS SYSTEMS: A REVIEW OF THE GENERAL THEORY
- The geometry of resonance tongues: a singularity theory approach
- Normal-internal resonances in quasi-periodically forced oscillators: a conservative approach
- Second-order analysis in polynomially perturbed reversible quadratic Hamiltonian systems
- On the Continuation of an Invariant Torus in a Family with Rapid Oscillations
- Renormalization group for one-dimensional fermions. A review on mathematical results