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Torsion-adding and asymptotic winding number for periodic window sequences. (English) Zbl 1428.37061

Summary: In parameter space of nonlinear dynamical systems, windows of periodic states are aligned following the routes of period-adding configuring periodic window sequences. In state space of driven nonlinear oscillators, we determine the torsion associated with the periodic states and identify regions of uniform torsion in the window sequences. Moreover, we find that the measured torsion differs by a constant between successive windows in periodic window sequences. Finally, combining the torsion-adding phenomenon, reported in this work, and the known period-adding rule, we deduce a general rule to obtain the asymptotic winding number in the accumulation limit of such periodic window sequences.

MSC:

37J46 Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
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