Research projects

Project CEMAPRE internal

TitleSRB measures for piecewise diffeomorphisms
ParticipantsDavide Azevedo, José Pedro Gaivão, João Lopes Dias (Principal Investigator)
SummaryOne type of behaviour that often arises in a dynamical system is the so-called chaotic motion. It
refers to complex and unpredictable dynamics arising even in the simplest non-linear models
(iteration of non-linear functions). Initially close orbits get exponentially far from each other as
time advances. As a consequence, one cannot hope to obtain explicit solutions but only statistical
characterization of the dynamics. It is therefore the existence of an invariant probability measure
that allows us to understand and classify the typical evolution of a system. In this project we want
to find conditions for the existence of a special type of invariant measures called SRB measures for
piecewise diffeomorphisms.