Homoclinic orbits for a singular second order hamiltonian system
Homoclinic orbits in a two-patch predator-prey model with Preisach hysteresis operator
Systems of operator-differential equations with hysteresis operators can have unstable equilibrium points with an open basin of attraction. Such equilibria can have homoclinic orbits attached to them, and these orbits are robust. In this paper a population dynamics model with hysteretic response of the prey to variations of the predator is introduced. In this model the prey moves between two patches, and the derivative of the Preisach operator is used to describe the hysteretic flow between the...
Homoclinic orbits on non-compact riemannian manifolds for second order hamiltonian systems
Homoclinic Points in Conservative Systems.
Homoclinic solutions for a class of second order non-autonomous systems.
Homoclinic solutions for second-order non-autonomous Hamiltonian systems without global Ambrosetti-Rabinowitz conditions.
Homoclinic solutions of 2nth-order difference equations containing both advance and retardation
By using the critical point method, some new criteria are obtained for the existence and multiplicity of homoclinic solutions to a 2nth-order nonlinear difference equation. The proof is based on the Mountain Pass Lemma in combination with periodic approximations. Our results extend and improve some known ones.
Homoclinic tangencies and hyperbolicity for surface diffeomorphisms.
Homoclinic tangencies near cascades of period doubling bifurcations
Homoclinics : Poincaré-Melnikov type results via a variational approach
Homogeneous and isotropic statistical solutions of the Navier-Stokes equations.
Homogeneous polynomial vector fields of degree 2 on the 2-dimensional sphere.
Let X be a homogeneous polynomial vector field of degree 2 on S2 having finitely many invariant circles. Then, we prove that each invariant circle is a great circle of S2, and at most there are two invariant circles. We characterize the global phase portrait of these vector fields. Moreover, we show that if X has at least an invariant circle then it does not have limit cycles.
Homological Identities for Closed Orbits.
Homologie des géodésiques fermées sur des variétés hyperboliques avec bouts cuspidaux
Homology of origamis with symmetries
Given an origami (square-tiled surface) with automorphism group , we compute the decomposition of the first homology group of into isotypic -submodules. Through the action of the affine group of on the homology group, we deduce some consequences for the multiplicities of the Lyapunov exponents of the Kontsevich-Zorich cocycle. We also construct and study several families of interesting origamis illustrating our results.
Homomorphisms of the Lie algebras associated with a symplectic manifold
Homotopical dynamics II : Hopf invariants, smoothings and the Morse complex
Homotopical dynamics of gradient flows
In this paper we will be interested in results surrounding the following basic question: what are the homotopy properties that one can extract from a gradient flow? We approach this question by decomposing it into three parts: 1. Identify what are the homotopical objects that are provided by the flow (e.g. critical points, Conley indexes). 2. Discover what are the relations that have to be satisfied by these objects (e.g. Morse inequalities, Lusternik-Schnirelmann type inequalities). 3. (The Realizability...
Homotopy and dynamics for homeomorphisms of solenoids and Knaster continua
We describe the homotopy classes of self-homeomorphisms of solenoids and Knaster continua. In particular, we demonstrate that homeomorphisms within one homotopy class have the same (explicitly given) topological entropy and that they are actually semi-conjugate to an algebraic homeomorphism in the case when the entropy is positive.
Hopf bifurcation analysis for the van der Pol equation with discrete and distributed delays.