A generalized Poincaré-Birkhoff theorem with applications to coaxial vortex ring motion

Document Type

Article

Publication Date

1-1-2005

Abstract

A new generalization of the Poincaré-Birkhoff fixed point theorem applying to small perturbations of finite-dimensional, completely integrable Hamiltonian systems is formulated and proved. The motivation for this theorem is an extension of some recent results of Blackmore and Knio on the dynamics of three coaxial vortex rings in an ideal fluid. In particular, it is proved using KAM theory and this new fixed point theorem that if n > 3 coaxial rings all having vortex strengths of the same sign are initially in certain positions sufficiently close to one another in a three-dimensional ideal fluid environment, their motion with respect to the center of vorticity exhibits invariant (n - 1)-dimensional tori comprised of quasiperiodic orbits together with interspersed periodic trajectories.

Identifier

15844431967 (Scopus)

Publication Title

Discrete and Continuous Dynamical Systems Series B

External Full Text Location

https://doi.org/10.3934/dcdsb.2005.5.15

ISSN

15313492

First Page

15

Last Page

33

Issue

1

Volume

5

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