Isochronous properties in fractal analysis of some planar vector fields

DOI10.1016/j.bulsci.2010.03.006zbMath1214.37012OpenAlexW1969778664MaRDI QIDQ616308

Hao Wu, Weigu Li

Publication date: 7 January 2011

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2010.03.006

zbMATH Keywords

normal formfractal analysisisochronous foci

Mathematics Subject Classification ID

Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Dynamics induced by flows and semiflows (37C10) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

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Cites Work

• Normal forms for periodic orbits of real vector fields
• Characterizing isochronous points and computing isochronous sections
• The monotonicity of the period function for planar Hamiltonian vector fields
• Characterizing isochronous centres by Lie brackets
• Generating limit cycles from a nilpotent critical point via normal forms
• Fractal analysis of spiral trajectories of some planar vector fields
• On the critical periods of perturbed isochronous centers
• Stability of motion
• Extension of Floquet's theory to nonlinear periodic differential systems and embedding diffeomorphisms in differential flows
• Finitely-smooth normal forms of local families of diffeomorphisms and vector fields
• Characterization of isochronous foci for planar analytic differential systems