## Institute of Mathematical Statistics Lecture Notes - Monograph Series

### Nearly-integrable perturbations of the Lagrange top: applications of KAM-theory

#### Abstract

Motivated by the Lagrange top coupled to an oscillator, we consider the quasi-periodic Hamiltonian Hopf bifurcation. To this end, we develop the normal linear stability theory of an invariant torus with a generic (i.e., non-semisimple) normal $1:-1$ resonance. This theory guarantees the persistence of the invariant torus in the Diophantine case and makes possible a further quasi-periodic normal form, necessary for investigation of the non-linear dynamics. As a consequence, we find Cantor families of invariant isotropic tori of all dimensions suggested by the integrable approximation.

#### Chapter information

Source
Dee Denteneer, Frank den Hollander, Evgeny Verbitskiy, eds., Dynamics & Stochastics: Festschrift in honor of M. S. Keane (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), >286-303

Dates
First available in Project Euclid: 28 November 2007

https://projecteuclid.org/euclid.lnms/1196285829

Digital Object Identifier
doi:10.1214/074921706000000301

Mathematical Reviews number (MathSciNet)
MR2306209

Zentralblatt MATH identifier
1125.70003

Rights