Geodesic
Poincar\'e recurrences in a stroboscopic section of a nonautonomous van der Pol oscillator
Russian journal of nonlinear dynamics, Tome 10 (2014) no. 2, pp. 149-156

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In the present work we analyze the statistics of a set that is obtained by calculating a stroboscopic section of phase trajectories in a harmonically driven van der Pol oscillator. It is shown that this set is similar to a linear shift on a circle with an irrational rotation number, which is defined as the detuning between the external and natural frequencies. The dependence of minimal return times on the size $\varepsilon$ of the return interval is studied experimentally for the golden ratio. Furthermore, it is also found that in this case, the value of the Afraimovich–Pesin dimension is $\alpha_c=1$.
Keywords: Poincaré recurrence, Afraimovich–Pesin dimension, Fibonacci stairs, circle map, van der Pol oscillator. 
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     author = {Nadezhda I. Semenova and Vadim S. Anishchenko},
     title = {Poincar\'e recurrences in a stroboscopic section of a nonautonomous van der {Pol} oscillator},
     journal = {Russian journal of nonlinear dynamics},
     pages = {149--156},
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     number = {2},
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     url = {http://geodesic.mathdoc.fr/item/ND_2014_10_2_a1/}
}
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Nadezhda I. Semenova; Vadim S. Anishchenko. Poincar\'e recurrences in a stroboscopic section of a nonautonomous van der Pol oscillator. Russian journal of nonlinear dynamics, Tome 10 (2014) no. 2, pp. 149-156. http://geodesic.mathdoc.fr/item/ND_2014_10_2_a1/