Periodic solutions of second order hamiltonian systems bifurcating from infinity
Some existence and multiplicity results for periodic solutions of second order nonautonomous systems with the potentials changing sign are presented. The proofs of the existence results rely on the use of a linking theorem and the Mountain Pass theorem by Ambrosetti and Rabinowitz [2]. The multiplicity results are deduced by the study of constrained critical points of minimum or Mountain Pass type.
In this paper we obtain results on existence of non-constant periodic traveling waves with arbitrary speed in infinite system of linearly coupled nonlinear oscillators on a two-dimensional lattice. Sufficient conditions for the existence of such solutions are obtained with the aid of critical point method and linking theorem.
Given β > 1, let TβThe iteration of this transformation gives rise to the greedy β-expansion. There has been extensive research on the properties of this expansion and its dependence on the parameter β.In [17], K. Schmidt analyzed the set of periodic points of Tβ, where β is a Pisot number. In an attempt to generalize some of his results, we study, for certain Pisot units, a different expansion that we call linear expansionwhere each ei...
The aim of this paper is to describe the set of periods of a Morse-Smale diffeomorphism of the two-dimensional sphere according to its homotopy class. The main tool for proving this is the Lefschetz fixed point theory.
For a smooth curve and a set in the plane , let be the space of finite Borel measures in the plane supported on , absolutely continuous with respect to the arc length and whose Fourier transform vanishes on . Following [12], we say that is a Heisenberg uniqueness pair if . In the context of a hyperbola , the study of Heisenberg uniqueness pairs is the same as looking for uniqueness sets of a collection of solutions to the Klein-Gordon equation. In this work, we mainly address the...
On se propose de montrer que les variétés à bord et plus généralement à coins, normalement dilatées par un endomorphisme sont persistantes en tant que stratifications -régulières. Ce résultat sera démontré en classe , pour . On donne aussi un exemple simple d’une sous-variété à bord normalement dilatée mais qui n’est pas persistante en tant que sous-variété différentiable.