Bifurcations de points fixes elliptiques. III: Orbites périodiques de ``petites périodes et élimination résonnante des couples de courbes invariantes. (Bifurcations of elliptic fixed points. III: Periodic orbits with ``small periods and resonant e

DOI10.1007/BF02698927zbMath0712.58044OpenAlexW1580206188MaRDI QIDQ748988

Alain Chenciner

Publication date: 1988

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=PMIHES_1987__66__5_0

zbMATH Keywords

diffeomorphismiterationinvariant setsbifurcationperiodic orbitrotation numberresonancemap

Mathematics Subject Classification ID

Forced motions for nonlinear problems in mechanics (70K40) Normal forms for dynamical systems (37G05) Local and nonlocal bifurcation theory for dynamical systems (37G99) Differential topological aspects of diffeomorphisms (57R50)

Related Items (20)

Dédoublement de courbes invariantes sur le cylindre: petits diviseurs. (Small divisors phenomena in an invariant curve doubling bifurcation on a cylinder) ⋮ Chenciner bubbles and torus break-up in a periodically forced delay differential equation ⋮ Singularities in dynamics: a catastrophic viewpoint ⋮ A normal form à la Moser for diffeomorphisms and a generalization of Rüssmann's translated curve theorem to higher dimensions ⋮ Two-parameter bifurcations in LPA model ⋮ Pitchfork bifurcations of invariant manifolds ⋮ Resonance and fractal geometry ⋮ Attractive invariant circles à la Chenciner ⋮ Quasi-periodic bifurcations of invariant circles in low-dimensional dissipative dynamical systems ⋮ Resonant tori, transport barriers, and chaos in a vector field with a Neimark-Sacker bifurcation ⋮ Normal resonances in a double Hopf bifurcation ⋮ Hopf saddle-node bifurcation for fixed points of 3D-diffeomorphisms: Analysis of a resonance `bubble' ⋮ Analysis of Degenerate Chenciner Bifurcation ⋮ Degenerate Chenciner Bifurcation Revisited ⋮ Boundary of two frequency behaviour in a system of three weakly coupled electronic oscillators ⋮ On the quasi-periodic \(d\)-fold degenerate bifurcation ⋮ Remarks on interacting Neimark–Sacker bifurcations ⋮ Mixed spectra and rotational symmetry ⋮ Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos ⋮ Resonance and Singularities

Cites Work

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• Bifurcations de points fixes elliptiques. I: Courbes invariantes
• Bifurcations de points fixes elliptiques. II: Orbites periodiques et ensembles de Cantor invariants. (Bifurcations of elliptic fixed points. II: Periodic orbits and invariant Cantor sets)
• Existence d'orbites quasi-périodiques dans les attracteurs de Birkhoff. (Existence of quasiperiodic orbits in Birkhoff attractors)
• Bifurcations from an invariant circle for two-parameter families of maps of the plane: a computer-assisted study
• Germs of diffeomorphisms in the plane
• Invariant circles and the order structure of periodic orbits in monotone twist maps
• Nonexistence of integrals for canonical systems of differential equations
• Homoclinic points near elliptic fixed points

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