We present a description of isochronous centres of planar vector fields $X$ by means of their groups of symmetries. More precisely, given a normalizer $U$ of $X$ (i.e., $[X,U]=\mu X$, where $\mu$ is a scalar function), we ...

One of the fundamental problems in dynamical systems is the detection and characterisation of chaotic behaviours. In this work we will focus on chaos induced by what is called the Smale horseshoe. Smale horseshoes frequently ...

We present an example of a smooth invertible contraction in aninfinite-dimensional Hilbert space that is not locally ${\mathcalC}^{1}$-linearizable near its fixed point.

Desenvolupament d'un model 2-dimensional per el sistema coorbital de Janus i Epimetheus al voltant de Saturn, afegint l'aplanament del planeta. Demostracio d'un teorema de simetries sobre les equacions de moviment i analisi ...

The goal of this thesis is to show that chaotic orbits of a dynamical system are advantageous (compared with regularnes) to determine the characteristic parameters of the system, and to give an estimate about the behaviour ...

Summary. The aim of this paper is to give an axiomatic definition of the topological entropy for continuous interval maps and, in such a way, to shed some more light on the importance of the different properties of the ...

The Communication Through Coherence (CTC) theory establishes that neural communication is much effective if the underlying oscillatory activity of both populations are phase locked, that is, the input from the emitting ...

Interval analysis is presented as a solution to obtain rigorous results using computers. We present a methodology of computer-assisted proofs which involves the use of interval computations. In this thesis we introduce the ...

We consider differentiable maps having an invariant torus with normal behavior having a central part. We prove the existence and regularity of pseudostable manifolds and regularity with respect to parameters. Then we ...