title: Fibonacci stairs and the Afraimovich-Pesin dimension for a stroboscopic section of a nonautonomous van der Pol oscillator.
abstract: Statistics of Poincaré recurrences is studied in the stroboscopic section of trajectories of a nonautonomous van der Pol oscillator in the framework of the global approach. It is shown that when the oscillator frequency and the frequency of the external force are irrationally related, the set obtained stroboscopically is equivalent to the circle map. For small values of the external amplitude, the Fibonacci stairs is constructed for the golden and silver ratios and its universal properties are confirmed. It is established that the Afraimovich-Pesin dimension for the map in the stroboscopic section is αc = 1 for Diophantine irrational rotation numbers.
authors.affiliation: Department of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia.
authors.forename: Nadezhda I
authors.initials: NI
authors.lastname: Semenova
authors.affiliation: Department of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia.
authors.forename: Vadim S
authors.initials: VS
authors.lastname: Anishchenko