Hofer's L...-geometry: energy and stability of Hamiltonian flows, part II (Erratum).
Hofer’s metrics and boundary depth
We show that if is a closed symplectic manifold which admits a nontrivial Hamiltonian vector field all of whose contractible closed orbits are constant, then Hofer’s metric on the group of Hamiltonian diffeomorphisms of has infinite diameter, and indeed admits infinite-dimensional quasi-isometrically embedded normed vector spaces. A similar conclusion applies to Hofer’s metric on various spaces of Lagrangian submanifolds, including those Hamiltonian-isotopic to the diagonal in when satisfies...
Holomorphic Anosov systems.
Holomorphic flows and complex structures on products of odd dimensional spheres.
Holomorphic foliations by curves on with non-isolated singularities
Let be a holomorphic foliation by curves on . We treat the case where the set consists of disjoint regular curves and some isolated points outside of them. In this situation, using Baum-Bott’s formula and Porteuos’theorem, we determine the number of isolated singularities, counted with multiplicities, in terms of the degree of , the multiplicity of along the curves and the degree and genus of the curves.
Holomorphic foliations in having an invariant algebraic curve
We give estimations for the degree of separatrices of algebraic foliations in .
Holomorphic Lagrangian bundles over flag manifolds.
Holomorphic solutions to linear first-order functional differential equations.
Holomorphic symplectic normalization of a real function
Homeomorphisms of composants of Knaster continua
The Knaster continuum is defined as the inverse limit of the pth degree tent map. On every composant of the Knaster continuum we introduce an order and we consider some special points of the composant. These are used to describe the structure of the composants. We then prove that, for any integer p ≥ 2, all composants of having no endpoints are homeomorphic. This generalizes Bandt’s result which concerns the case p = 2.
Homeomorphisms of inverse limit spaces of one-dimensional maps
We present a new technique for showing that inverse limit spaces of certain one-dimensional Markov maps are not homeomorphic. In particular, the inverse limit spaces for the three maps from the tent family having periodic kneading sequence of length five are not homeomorphic.
Homoclinic and periodic orbits for hamiltonian systems
Homoclinic bifurcations and uniform hyperbolicity for three-dimensional flows
Homoclinic orbit solutions of a one dimensional Wilson-Cowan type model.
Homoclinic orbits for a class of singular second order Hamiltonian systems in ℝ3
We consider a conservative second order Hamiltonian system in ℝ3 with a potential V having a global maximum at the origin and a line l ∩ 0 = ϑ as a set of singular points. Under a certain compactness condition on V at infinity and a strong force condition at singular points we study, by the use of variational methods and geometrical arguments, the existence of homoclinic solutions of the system.
Homoclinic orbits for a class of symmetric Hamiltonian systems.
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.