We consider stochastic processes arising from dynamical systems by evaluating an observable function along the orbits of the system. We will consider observables that achieve a global maximum value at multiple points, all belonging to the orbit of the same point, which may be periodic or not. We will see what impact this has on the Extremal Index and clustering patterns when compared to the case where the maximum is achieved in a single point. In particular we will observe the appearance of clustering not caused by periodic orbits.
(Joint work with A. C. M. Freitas, J. M. Freitas and F.B. Rodrigues.) |