Complex Systems Seminar Dynamical properties of superstable attractors in the logistic map

Date
2006-12-06 13:00 - 2006-12-06 14:30
Place
N508, RIES, Hokkaido University
Speaker/Organizer
Luis Moyano (Centro Brasileiro de Pesquisas Fsicas, Brazil)
 
In this talk I will present previously unknown properties of thefamily of periodic superstable cycles characterized by a Lyapunovexponent that diverges to minus infinity. The successive superstablecycles illustrate the fractal structure of the Feibenbaum attractor.We will show that the basin of attraction for the phases of the cyclesdevelops fractal boundaries of increasing complexity as theperiod-doubling structure advances towards the transition to chaos. Wewill also comment on the dynamical features of the trajectories thateither evolve towards the Feigenbaum attractor or are captured by itsmatching repellor.