Abstract:
Generalized standard maps of the cylinder for which the rotation number is a rational function (a combination of the Fermi and Chirikov rotation functions) are considered. These symplectic maps often have degenerate resonant zones, and we establish two types resonance bifurcations: "loops" and "vortex pairs". Both the border of chaos and the existence of the chaotic web are discussed. Finally the transition to global chaos for a generalized map is considered.
\Bibitem{HowMor12}
\by James E. Howard, Albert D. Morozov
\paper A Simple Reconnecting Map
\jour Regul. Chaotic Dyn.
\yr 2012
\vol 17
\issue 5
\pages 417--430
\mathnet{http://mi.mathnet.ru/rcd412}
\crossref{https://doi.org/10.1134/S1560354712050048}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2989514}
\zmath{https://zbmath.org/?q=an:1279.37021}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2012RCD....17..417H}
Linking options:
https://www.mathnet.ru/eng/rcd412
https://www.mathnet.ru/eng/rcd/v17/i5/p417
This publication is cited in the following 5 articles:
K. E. Morozov, A. D. Morozov, “Degenerate Resonances and Synchronization of Quasiperiodic Oscillations”, J Math Sci, 269:6 (2023), 823
Albert D. Morozov, Kirill E. Morozov, “Degenerate Resonances and Synchronization in Nearly
Hamiltonian Systems Under Quasi-periodic Perturbations”, Regul. Chaotic Dyn., 27:5 (2022), 572–585
Morozov A.D., Morozov K.E., “Synchronization of Quasiperiodic Oscillations in Nearly Hamiltonian Systems: the Degenerate Case”, Chaos, 31:8 (2021), 083109
K. E. Morozov, A. D. Morozov, “Quasiperiodic Perturbations of Twodimensional Hamiltonian Systems with Nonmonotone Rotation”, J Math Sci, 255:6 (2021), 741
Albert D. Morozov, “On Bifurcations in Degenerate Resonance Zones”, Regul. Chaotic Dyn., 19:4 (2014), 474–482
Citation in format AMSBIB
Contact us: