Higher order Poincaré-Pontryagin functions and iterated path integrals
Higher order Schwarzian derivatives in interval dynamics
We introduce an infinite sequence of higher order Schwarzian derivatives closely related to the theory of monotone matrix functions. We generalize the classical Koebe lemma to maps with positive Schwarzian derivatives up to some order, obtaining control over derivatives of high order. For a large class of multimodal interval maps we show that all inverse branches of first return maps to sufficiently small neighbourhoods of critical values have their higher order Schwarzian derivatives positive up...
Higher period stochastic bifurcation of nonlinear airfoil fluid-structure interaction.
Higher-order equations of the KdV type are integrable.
Higher-order KdV-type equations and their stability.
Higher-order Melnikov functions for single-DOF mechanical oscillators: theoretical treatment and applications.
Highest Weight Modules of W1+∞, Darboux Transformations and the Bispectral Problem
This paper is a survey of our recent results on the bispectral problem. We describe a new method for constructing bispectral algebras of any rank and illustrate the method by a series of new examples as well as by all previously known ones. Next we exhibit a close connection of the bispectral problem to the representation theory of W1+∞–algerba. This connection allows us to explain and generalise to any rank the result of Magri and Zubelli on the symmetries of the manifold of the bispectral operators...
High-order phase transitions in the quadratic family
We give the first example of a transitive quadratic map whose real and complex geometric pressure functions have a high-order phase transition. In fact, we show that this phase transition resembles a Kosterlitz-Thouless singularity: Near the critical parameter the geometric pressure function behaves as near , before becoming linear. This quadratic map has a non-recurrent critical point, so it is non-uniformly hyperbolic in a strong sense.
Hofer's L...-geometry: energy and stability of Hamiltonian flows, part I.
Hofer's L...-geometry: energy and stability of Hamiltonian flows, part II.
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.