THE STRUCTURE OF PHASE SPACE CLOSE TO FIXED POINTS IN A 4D SYMPLECTIC MAP

DOI10.1142/S0218127413300231zbMath1275.37027arXiv1205.4575OpenAlexW3104872878MaRDI QIDQ2864931

Loukas Zachilas, Matthaios Katsanikas, P. A. Patsis

Publication date: 27 November 2013

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

Full work available at URL: https://arxiv.org/abs/1205.4575

zbMATH Keywords

chaos and dynamical systems4D symplectic maps

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45)

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Cites Work

• Motion close to the Hopf bifurcation of the vertical family of periodic orbits of \(L_{4}\)
• INSTABILITIES AND STICKINESS IN A 3D ROTATING GALACTIC POTENTIAL
• THE STRUCTURE OF INVARIANT TORI IN A 3D GALACTIC POTENTIAL
• THE STRUCTURE AND EVOLUTION OF CONFINED TORI NEAR A HAMILTONIAN HOPF BIFURCATION
• Structure and Breakdown of Invariant Tori in a 4-D Mapping Model of Accelerator Dynamics
• 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
• PROBING THE LOCAL DYNAMICS OF PERIODIC ORBITS BY THE GENERALIZED ALIGNMENT INDEX (GALI) METHOD