Families of periodic orbits: local continuability does not imply global continuability

DOI10.4310/jdg/1214436225zbMath0487.58022OpenAlexW1581044076WikidataQ115188225 ScholiaQ115188225MaRDI QIDQ1165504

Kathleen T. Alligood, John Mallet-Paret, James A. Yorke

Publication date: 1981

Published in: Journal of Differential Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4310/jdg/1214436225

zbMATH Keywords

Hopf bifurcationperiod doublingfamilies of periodic orbitsMoebius orbitglobal continuabilitylocal continuabilityparametrized zeroes

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Degree, winding number (55M25) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (13)

On the global structure of period doubling flows ⋮ Generic \(S^ 1\)-equivariant vector fields ⋮ Global Hopf bifurcation of two-parameter flows ⋮ A Canonical Partition of the Periodic Orbits of Chaotic Maps ⋮ John Mallet-Paret 60 ⋮ Families of periodic orbits: closed 1-forms and global continuability ⋮ The existence of periodic travelling waves for singularly perturbed predator prey equations via the Conley index ⋮ Snakes: oriented families of periodic orbits, their sources, sinks, and continuation ⋮ \(S^ 1\)-degree and global Hopf bifurcation theory of functional differential equations ⋮ Cascades of period-doubling bifurcations: A prerequisite for horseshoes ⋮ Global Families of Limit Cycles of Planar Analytic Systems ⋮ On the continuability of periodic orbits of parametrized three- dimensional differential equations ⋮ Families of periodic orbits: Virtual periods and global continuability

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