17 citations · 30 across the 9 of their papers we have counts for
6 papers · 1 filter
Normal-normal resonances in a double Hopf bifurcation
Henk Broer, Heinz Hanßmann, Florian Wagener
We investigate the stability loss of invariant n-dimensional quasi-periodic tori during a double Hopf bifurcation, where at bifurcation the two normal frequencies are in normal-nor…
Bifurcations and Monodromy of the Axially Symmetric 1:1:-2 Resonance
Konstantinos Efstathiou, Heinz Hanßmann, Antonella Marchesiello
We consider integrable Hamiltonian systems in three degrees of freedom near an elliptic equilibrium in 1:1:-2 resonance. The integrability originates from averaging along the perio…
The 1:1 resonance in Hamiltonian systems
Heinz Hanssmann, Igor Hoveijn
Two-degree-of-freedom Hamiltonian systems with an elliptic equilibrium at the origin are characterised by the frequencies of the linearisation. Considering the frequencies as param…
The degenerate C. Neumann system I: symmetry reduction and convexity
Holger R. Dullin, Heinz Hanßmann
The C. Neumann system describes a particle on the sphere S^n under the influence of a potential that is a quadratic form. We study the case that the quadratic form has l+1 distinct…
Quasi-periodic stability of normally resonant tori
Henk W. Broer, M. Cristina Ciocci, Heinz Hanßmann +1
We study quasi-periodic tori under a normal-internal resonance, possibly with multiple eigenvalues. Two non-degeneracy conditions play a role. The first of these generalizes invert…
Nearly-integrable perturbations of the Lagrange top: applications of KAM-theory
H. W. Broer, H. Hanßmann, J. Hoo +1
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 a…