Limit cycles and Lie symmetries

DOI10.1016/j.bulsci.2006.03.015zbMath1121.37023OpenAlexW2046686039MaRDI QIDQ2384454

Armengol Gasull, Antoni Guillamon, Emilio Freire

Publication date: 21 September 2007

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

Full work available at URL: https://doi.org/10.1016/j.bulsci.2006.03.015

zbMATH Keywords

hyperbolicityisochrons

Mathematics Subject Classification ID

Geometric methods in ordinary differential equations (34A26) Symmetries, invariants of ordinary differential equations (34C14) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Periodic orbits of vector fields and flows (37C27)

Related Items (7)

Centralizers and normalizers of local analytic and formal vector fields ⋮ Geometric tools to determine the hyperbolicity of limit cycles ⋮ On the critical points of the flight return time function of perturbed closed orbits ⋮ Effectiveness of the Bendixson-Dulac theorem ⋮ Perturbed normalizers and Melnikov functions ⋮ The number of limit cycles in planar systems and generalized Abel equations with monotonous hyperbolicity ⋮ Local orthogonal rectification: deriving natural coordinates to study flows relative to manifolds

Cites Work

• Isochrons and phaseless sets
• Patterns of phase compromise in biological cycles
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• Period function for perturbed isochronous centres.
• A characterization of isochronous centres in terms of symmetries.
• First derivative of the period function with applications
• Asymptotic phase revisited
• regularity properties of the period function near a center of a planar vector field
• Non-linear dynamic systems, limit cycles, transformation groups, and perturbation techniques
• Limit cycles as invariant functions of Lie groups
• ISOCHRONOUS SECTIONS VIA NORMALIZERS
• Geometrical conditions for the stability of orbits in planar systems
• The geometry of biological time.
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