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Generalized iterated function systems, multifunctions and Cantor sets

Maciej Klimek, Marta Kosek (2009)

Annales Polonici Mathematici

Using a construction similar to an iterated function system, but with functions changing at each step of iteration, we provide a natural example of a continuous one-parameter family of holomorphic functions of infinitely many variables. This family is parametrized by the compact space of positive integer sequences of prescribed growth and hence it can also be viewed as a parametric description of a trivial analytic multifunction.

Generalized PN manifolds and separation of variables

Fernand Pelletier, Patrick Cabau (2008)

Banach Center Publications

The notion of generalized PN manifold is a framework which allows one to get properties of first integrals of the associated bihamiltonian system: conditions of existence of a bi-abelian subalgebra obtained from the momentum map and characterization of such an algebra linked with the problem of separation of variables.

Generalized recurrence, compactifications, and the Lyapunov topology

Ethan Akin, Joseph Auslander (2010)

Studia Mathematica

We study generalized recurrence for closed relations on locally compact spaces. This includes continuous maps and real flows. The main tools are Lyapunov functions and their compactifications. Under certain conditions it is shown that the Lyapunov functions determine the topology of the space.

Generalized Staircases: Recurrence and Symmetry

W. Patrick Hooper, Barak Weiss (2012)

Annales de l’institut Fourier

We study infinite translation surfaces which are ℤ -covers of compact translation surfaces. We obtain conditions ensuring that such surfaces have Veech groups which are Fuchsian of the first kind and give a necessary and sufficient condition for recurrence of their straight-line flows. Extending results of Hubert and Schmithüsen, we provide examples of infinite non-arithmetic lattice surfaces, as well as surfaces with infinitely generated Veech groups.

Generalized synchronization in a system of several non-autonomous oscillators coupled by a medium

Rogério Martins, Gonçalo Morais (2015)

Kybernetika

An abstract theory on general synchronization of a system of several oscillators coupled by a medium is given. By generalized synchronization we mean the existence of an invariant manifold that allows a reduction in dimension. The case of a concrete system modeling the dynamics of a chemical solution on two containers connected to a third container is studied from the basics to arbitrary perturbations. Conditions under which synchronization occurs are given. Our theoretical results are complemented...

Générateurs indépendants pour les systèmes d'isométries de dimension un

Damien Gaboriau (1997)

Annales de l'institut Fourier

Un système fini d’isométries partielles de R est dit à générateurs indépendants si les composés non triviaux fixent au plus un point. On décrit un procédé simple et naturel pour obtenir des générateurs indépendants, sans modifier les orbites, pour tout système sans composante minimale homogène : en prenant la restriction de chaque générateur à un certain sous-intervalle de son domaine. Un système avec une composante minimale homogène ne possède pas de générateurs indépendants.

Generic bifurcation of reversible vector fields on a 2-bidimensional manifold.

Marco Antonio Teixeira (1997)

Publicacions Matemàtiques

In this paper we deal with reversible vector fields on a 2-dimensional manifold having a codimension one submanifold as its symmetry axis. We classify generically the one parameter families of such vector fields. As a matter of fact, aspects of structural stability and codimension one bifurcation are analysed.

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