The invariance of the algebraic multiplicity of a holomorphic vector field
We prove that the algebraic multiplicity of a holomorphic vector field at an isolated singularity is invariant by equivalences.
The hypothesis in Pesin theory
The canonical structure of the supersymmetric non-linear σ model in the constrained hamiltonian formalism
The capacity of parabolic Julia sets.
The Cauchy problem for the Gross–Pitaevskii equation
The centralizer of Morse shifts
The centralizer of Morse shifts induced by arbitrary blocks
The chain recurrent set for maps of compacta
For a self-map of a compactum we give a necessary and sufficient condition for the chain recurrent set to be precisely the set of periodic points.
The characteristic variety of a generic foliation
We confirm a conjecture of Bernstein–Lunts which predicts that the characteristic variety of a generic polynomial vector field has no homogeneous involutive subvarieties besides the zero section and subvarieties of fibers over singular points.
The Circle Problem on Surfaces of Variable Negative Curvature.
The classification of circle-like continua that admit expansive homeomorphisms
A homeomorphism h: X → X of a compactum X is expansive provided that for some fixed c > 0 and every x, y ∈ X (x ≠ y) there exists an integer n, dependent only on x and y, such that d(hⁿ(x),hⁿ(y)) > c. It is shown that if X is a solenoid that admits an expansive homeomorphism, then X is homeomorphic to a regular solenoid. It can then be concluded that a circle-like continuum admits an expansive homeomorphism if and only if it is homeomorphic to a regular solenoid.
The classification of tiling space flows.
The coexistence problem" for conservative dynamical systems: a review
The cohomological equation for area-preserving flows on compact surfaces.
The compact category and mulitple periodic solutions of Hamiltionian systems on symmetric starshaped energy surfaces.
The complex geometry of the Kowalewski-Painlevé analysis.
The conjugacy between Cascades generated by a weakly nonlinear system and the Euler method of a flow
Sufficient conditions for the existence of a topological conjugacy between a cascade obtained from a weakly nonlinear flow by fixing the time step and a cascade obtained by the Euler method are analysed. The aim of this paper is to provide relations between constants in the Fečkan theorem. Given such relations an implementation of a weakly nonlinear neuron is possible.
The Conley index and countable decompositions of invariant sets
We define a new cohomological index of Conley type associated to any bi-infinite sequence of neighborhoods that satisfies a certain isolation condition. We use this index to study the chaotic dynamics on invariant sets which decompose as countable unions of pairwise disjoint (mod 0) compact pieces.
The Conley index for flows preserving generalized symmetries
Topological spaces with generalized symmetries are defined and extensions of the Conley index of a compact isolated invariant set of the flow preserving the structures introduced are proposed. One of the two new indexes is constructed with no additional assumption on the examined set in terms of symmetry invariance.
The Conley index over a space.