Sandra Vinagre

Iteration of Differentiable Functions under m-Modal Maps with Aperiodic Kneading Sequences

We consider the dynamical system (𝒜, 𝑇), where 𝒜 is a class of differentiable functions defined on some interval and 𝑇 : 𝒜 → 𝒜 is the operator 𝑇𝜙∶=𝑓∘𝜙, where 𝑓 is a differentiable m-modal map. Using an algorithm, we obtained some numerical and symbolic results related to the frequencies of occurrence of critical values of the iterated functions when the kneading sequences of 𝑓 are aperiodic. Moreover, we analyze the evolution as well as the distribution of the aperiodic critical values of the iterated functions.

THE BASIN OF ATTRACTION OF LOZI MAPPINGS

For parameter values which assure its existence, we characterize the basin of attraction for the Lozi map strange attractor.

COMPUTING TOPOLOGICAL INVARIANTS IN BOUNDARY VALUE PROBLEMS REDUCIBLE TO DIFFERENCE EQUATIONS

Among boundary values problems (BVP) for partial differential equations there are certain classes of problems reducible to difference equations. Effective study of such problems has became possible in the last 20-30 years owing to appreciable advances done also in the theory of difference equations with discrete time, specifically given by one-dimensional maps. Here we apply how this reduction method may be used in simple nonlinear BVP, determined by a bimodal map. We consider two-dimensional linear hyperbolic system with constant coefficients, with nonlinear boundary conditions and usual initial conditions. The objective is to characterize the dependence of the motions of the vortice solutions with the topological invariants of the bimodal map.

Asymptotic Behaviour in a Certain Nonlinearly Perturbed Heat Equation: Non Periodic Perturbation Case

We consider a system described by the linear heat equation with adiabatic boundary conditions. We impose a nonlinear perturbation determined by a family of interval maps characterized by a certain set of parameters. The time instants of the perturbation are determined by an additional dynamical system, seen here as part of the external interacting system. We analyse the complex behaviour of the system, through the scope of symbolic dynamics, and the dependence of the behaviour on the time pattern of the perturbation, comparing it with previous results in the periodic case.