We prove the existence of monoparametric families of multibreathers in chains of Hamiltonian oscillators of one degree of freedom, with the total energy of the chain as a parameter. At the same time we evaluate the neighborhood of the initial conditions for these solutions, as well as their stability. For the proof we use an idea originally proposed by Poincaré. We apply our results to calculate families of multibreathers in a chain consisting of coupled Morse oscillators.
The twist condition is a necessary condition in integrable Hamiltonian systems and symplectic maps to obtain Poincaré–Birkhoff bifurcations under small perturbations. When this condition does not hold, topological structures other than Poincaré–Birkhoff chains arise in phase space through bifurcations of isolated periodic orbits and reconnections of asymptotic manifolds. In this paper we construct an integrable model Hamiltonian with degeneracies suitable to observe these phenomena close to nontwist resonant tori. The generation of isochronous chains and the stability of their fixed points is determined analytically and a condition for the reconnection is found. Particular examples are given, illustrating the bifurcation and reconnection scenario for several cases of degeneracy.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.