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Invariant manifolds of degenerate tori and double parabolic orbits to infinity in the (n+2)-body problem
Immaculada Baldomá, Ernest Fontich, Pau Martín
There are many interesting dynamical systems in which degenerate invariant tori appear. We give conditions under which these degenerate tori have stable and unstable invariant mani…
Invariant manifolds of maps and vector fields with nilpotent parabolic tori
Clara Cufí-Cabré, Ernest Fontich
We consider analytic maps and vector fields defined in , having a -dimensional invariant torus . The map (resp. vector field) rest…
Functional shift-induced degenerate transcritical Neimark-Sacker bifurcation in a discrete hypercycle
E. Fontich, A. Guillamon, J. Perona +1
In this article we investigate the impact of functional shifts in a time-discrete cross-catalytic system. We use the hypercycle model considering that one of the species shifts fro…
Construction of invariant whiskered tori by a parameterization method. Part II: Quasi-periodic and almost periodic breathers in coupled map lattices
Ernest Fontich, Rafael de la Llave, Yannick Sire
We construct quasi-periodic and almost periodic solutions for coupled Hamiltonian systems on an infinite lattice which is translation invariant. The couplings can be long range, pr…