Quasi-periodic bifurcations of invariant circles in low-dimensional dissipative dynamical systems
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Publication:2430542
DOI10.1134/S1560354711010060zbMath1225.37087WikidataQ58117856 ScholiaQ58117856MaRDI QIDQ2430542
Renato Vitolo, Carles Simó, Henk W. Broer
Publication date: 7 April 2011
Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)
Computational methods for bifurcation problems in dynamical systems (37M20) Infinite nonwandering sets arising in bifurcations of dynamical systems (37G30) Periodic and quasi-periodic flows and diffeomorphisms (37C55)
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Uses Software
Cites Work
- A parametrised version of Moser's modifying terms theorem
- Resonance tongues and spectral gaps in quasi-periodic Schrödinger operators with one or more frequencies. A numerical exploration
- 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 elimination of pairs of invariant curves.)
- Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos
- Umbilical torus bifurcations in Hamiltonian systems
- A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: rigorous results
- Local and semi-local bifurcations in Hamiltonian dynamical systems. Results and examples
- Normal linear stability of quasi-periodic tori
- A parametrization method for the computation of invariant tori and their whiskers in quasi-periodic maps: numerical algorithms
- Hopf saddle-node bifurcation for fixed points of 3D-diffeomorphisms: Analysis of a resonance `bubble'
- Flow transitions resembling bifurcations of the logistic map in simulations of the baroclinic rotating annulus
- A mechanism for the fractalization of invariant curves in quasi-periodically forced 1-D maps
- A collocation method for the numerical Fourier analysis of quasi-periodic functions. I: Numerical tests and examples
- A collocation method for the numerical Fourier analysis of quasi-periodic functions. II: Analytical error estimates
- Quasi-periodic stability of normally resonant tori
- Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
- Bifurcations and stability of families of diffeomorphisms
- 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)
- Dédoublement de courbes invariantes sur le cylindre: petits diviseurs. (Small divisors phenomena in an invariant curve doubling bifurcation on a cylinder)
- Quasi-genericity of bifurcations to high dimensional invariant tori for maps
- Bifurcations de tores invariants
- The quasi-periodic centre-saddle bifurcation
- Mixed spectra and rotational symmetry
- Resonance tongues and instability pockets in the quasi-periodic Hill-Schrödinger equation
- Quasi-periodic stability of subfamilies of an unfolded skew Hopf bifurcation
- On the vertical families of two-dimensional tori near the triangular points of the bicircular problem
- Persistence properties of normally hyperbolic Tori
- On a quasi-periodic Hopf bifurcation
- Integrable and non-integrable deformations of the skew Hopf bifurcation
- Computation of invariant tori by Newton-Krylov methods in large-scale dissipative systems
- Parametric smoothness and self-scaling of the statistical properties of a minimal climate model: what beyond the mean field theories?
- Dynamics and geometry near resonant bifurcations
- Resonance tongues in the quasi-periodic Hill-Schrödinger equation with three frequencies
- The Hopf-saddle-node bifurcation for fixed points of 3D-diffeomorphisms: The Arnol'd resonance web
- On the quasi-periodic \(d\)-fold degenerate bifurcation
- The quasi-periodic doubling cascade in the transition to weak turbulence
- Dynamical systems and chaos
- Numerical computation of the normal behaviour of invariant curves ofn-dimensional maps
- Bifurcations and strange attractors in the Lorenz-84 climate model with seasonal forcing
- THE QUASI-PERIODIC REVERSIBLE HOPF BIFURCATION
- Generic Hopf–Neĭmark–Sacker bifurcations in feed-forward systems
- Routes to chaos in the Hopf-saddle-node bifurcation for fixed points of 3D-diffeomorphisms
- On the Computation of Reducible Invariant Tori on a Parallel Computer
- Nonnormally hyperbolic invariant curves for maps in R3and doubling bifurcation
- Towards global models near homoclinic tangencies of dissipative diffeomorphisms
- Hill's equation with quasi-periodic forcing: resonance tongues, instability pockets and global phenomena
- Normal-internal resonances in quasi-periodically forced oscillators: a conservative approach
- KAM theory without action-angle variables
- Resonances in skew and reducible quasi-periodic Hopf bifurcations
- On the Destruction of Resonant Lagrangean Tori in Hamiltonian Systems
- A Parameterization Method for the Computation of Invariant Tori and Their Whiskers in Quasi‐Periodic Maps: Explorations and Mechanisms for the Breakdown of Hyperbolicity
- Bifurcations of normally parabolic tori in Hamiltonian systems
- Direct numerical simulations of bifurcations in an air-filled rotating baroclinic annulus
- Continuation of Quasi-periodic Invariant Tori
- Unfoldings and bifurcations of quasi-periodic tori
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
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