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Some third‐order ordinary differential equations
Author(s) -
SwinnertonDyer Peter,
Wagenknecht Thomas
Publication year - 2008
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdn046
Subject(s) - mathematics , ordinary differential equation , dissipative system , mathematical analysis , differential algebraic equation , differential equation , periodic orbits , perturbation (astronomy) , fixed point , dynamical systems theory , poincaré–lindstedt method , singular perturbation , physics , quantum mechanics
The paper deals with periodic orbits in three systems of ordinary differential equations. Two of the systems, the Falkner–Skan equations and the Nosé equations, do not possess fixed points, and yet interesting dynamics can be found. Here, periodic orbits emerge in bifurcations from heteroclinic cycles, connecting fixed points at infinity. We present existence results for such periodic orbits and discuss their properties using careful asymptotic arguments. In the final part results about the Nosé equations are used to explain the dynamics in a dissipative perturbation, related to a system of dynamo equations.