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.
The Conley index theory: A brief introduction
A brief introduction to the Conley index theory is presented. The emphasis is the fundamental ideas of Conley's approach to dynamical systems and how it avoids some of the difficulties inherent in the study of nonlinear systems.
The Convergence of Zeta Functions for Certain Geodesic Flow Depends on Their Pressure.
The coupling of dynamics in couplied map lattices.
The cubic Szegő equation
We consider the following Hamiltonian equation on the Hardy space on the circle,where is the Szegő projector. This equation can be seen as a toy model for totally non dispersive evolution equations. We display a Lax pair structure for this equation. We prove that it admits an infinite sequence of conservation laws in involution, and that it can be approximated by a sequence of finite dimensional completely integrable Hamiltonian systems. We establish several instability phenomena illustrating...
The cyclic homology of
The cyclic spectrum of a Boolean flow.
The degenerate C. Neumann system I: symmetry reduction and convexity
The C. Neumann system describes a particle on the sphere S n under the influence of a potential that is a quadratic form. We study the case that the quadratic form has ℓ +1 distinct eigenvalues with multiplicity. Each group of m σ equal eigenvalues gives rise to an O(m σ)-symmetry in configuration space. The combined symmetry group G is a direct product of ℓ + 1 such factors, and its cotangent lift has an Ad*-equivariant momentum mapping. Regular reduction leads to the Rosochatius system on S ℓ,...
The Differentiable Structure of Three Remarkable Diffeomorphism Groups.
The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition
Consider a graph directed iterated function system (GIFS) on the line which consists of similarities. Assuming neither any separation conditions, nor any restrictions on the contractions, we compute the almost sure dimension of the attractor. Then we apply our result to give a partial answer to an open problem in the field of fractal image recognition concerning some self-affine graph directed attractors in space.
The dimension of the boundary of the Lévy dragon.
The direct Lyapunov method for an almost periodic difference system on a compactum.
The discovery of Smale horseshoe for dynamical system generated by autogenerator with tunnel diode
The dynamic complexity of a Holling type-IV predator-prey system with stage structure and double delays.
The Dynamical Complexity of Orientation Reversing Homeomorphisms of Surfaces.
The dynamics of complex polynomials and automorphisms of the shift.