Dresden 2009 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 27: Poster II

DY 27.22: Poster

Thursday, March 26, 2009, 16:00–18:00, P1B

Renyi Entropies of Quasi-Periodically Forced Nonlinear Systems — •Annette Witt — Max-Planck-Institute for Dynamics and Self-organization, Göttingen, Germany

Strange non-chaotic attractors (SNAs) which are characterized by a fractal geometry, although the underlining dynamics is non-chaotic, are typical for quasi-periodically forced nonlinear systems. In order to characterize the complex dynamics of these systems, their Renyi entropies K(q) are studied. Computational results are presented for time-discrete and time-continuous dynamical systems. Two types of dynamics on SNAs are found: (a) Homogeneous dynamics that is characterized by K(q)=0 for all crwoding indices q. (b) Non-homogeneous dynamics where the corresponding Renyi entropies decrease with q. Here, Renyi entropies K(q)=0 for all crowding indexes q>1 demonstrate the nonchaotic character of the considered systems. Moreover, positive Renyi entropies, K(q)>0, for crowding indexes q<q* with q*<1 stand for a fraction of exponentially expanding initially nearby trajectories. It is shown that this critical crowding index q* quantifies the ratio between regularity and chaos.