THE STRUCTURE AND EVOLUTION OF CONFINED TORI NEAR A HAMILTONIAN HOPF BIFURCATION

DOI10.1142/S0218127411029811zbMath1248.70017arXiv1012.2463MaRDI QIDQ3165836

Matthaios Katsanikas, George Contopoulos, P. A. Patsis

Publication date: 19 October 2012

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.2463

zbMATH Keywords

Hopf bifurcationgalactic dynamics4D surfaces of sectionchaos and dynamical systems

Mathematics Subject Classification ID

Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Hamilton's equations (70H05) Celestial mechanics (70F15) Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics (70H12)

Related Items (7)

Analytical and numerical manifolds in a symplectic 4-D map ⋮ STUDYING THE BASIN OF CONVERGENCE OF METHODS FOR COMPUTING PERIODIC ORBITS ⋮ Revealing roaming on the double Morse potential energy surface with Lagrangian descriptors ⋮ Visualizing the phase space of the HeI\(_2\) van der Waals complex using Lagrangian descriptors ⋮ Chaoticity in the vicinity of complex unstable periodic orbits in galactic type potentials ⋮ INSTABILITIES AND STICKINESS IN A 3D ROTATING GALACTIC POTENTIAL ⋮ THE STRUCTURE OF PHASE SPACE CLOSE TO FIXED POINTS IN A 4D SYMPLECTIC MAP

Uses Software

• Mathematica

Cites Work

• The Hamiltonian Hopf bifurcation
• THE STRUCTURE OF INVARIANT TORI IN A 3D GALACTIC POTENTIAL
• Quantitative estimates on the normal form around a non-semi-simple 1:−1 resonant periodic orbit
• Kolmogorov–Arnold–Moser aspects of the periodic Hamiltonian Hopf bifurcation
• Bifurcation at complex instability
• Simple three-dimensional periodic orbits in a galactic-type potential
• The stability of periodic orbits in the three-body problem
• USING COLOR AND ROTATION FOR VISUALIZING FOUR-DIMENSIONAL POINCARÉ CROSS-SECTIONS: WITH APPLICATIONS TO THE ORBITAL BEHAVIOR OF A THREE-DIMENSIONAL HAMILTONIAN SYSTEM
• Invariant curves near Hamiltonian–Hopf bifurcations of four-dimensional symplectic maps
• On the stability of periodic orbits of high dimensional autonomous Hamiltonian systems

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