@inproceedings{27f269fb5bac4551a1191e4637bdcf03,
title = "Nonintegrable perturbations of two vortex dynamics",
abstract = "The governing equations of motion of two point vortices in an ideal fluid in the plane has a Hamiltonian formulation that is completely integrable, so the dynamics are regular in the sense that one has quasiperiodic solutions confined to invariant two-dimensional tori accompanied by periodic orbits. Moreover, it is well known that the same is true of the dynamics of two point vortices in an ideal fluid in a standard half-plane (with a straight line boundary). It is natural to ask if this is also the case for half-planes whose boundaries are perturbations of a straight line. We prove here that there are such Hamiltonian perturbations of two vortex dynamics in the half-plane that generate chaotic - and a fortiori nonintegrable - dynamics, thereby answering an open question of rather long standing. Our proof, like most demonstrations of this kind, is based on Melnikov's method.",
keywords = "Chaos, Hamiltonian dynamics, Integrability, Melnikov's method, Transverse heteroclinic orbits",
author = "Denis Blackmore",
year = "2008",
doi = "10.1007/978-1-4020-6744-0_29",
language = "American English",
isbn = "9781402067433",
series = "Solid Mechanics and its Applications",
publisher = "Springer Verlag",
pages = "331--340",
booktitle = "IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Proceedings of the IUTAM Symposium",
address = "Germany",
note = "IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence ; Conference date: 25-08-2006 Through 30-08-2006",
}