Nonlinear Phenomena in Complex Systems, 2016, Vol.19, No.2, pp.207-210

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2016, Vol.19, No.2, pp.207-210

Invariant Wada Basins for One Periodic Second Order Differential Equation
Maria V. Makarova and Dmitry W. Serow<

A dissipative periodic second order differential equation with quadratic damping, cubic restoring force and with periodic coefficient at the even degree summand has been considered. Namely due to the periodic coefficient presence the invariant Wada basins with respect to the Poincar'e map has been obtained. The common boundary Wada basins and "ocean" is the Birkhoff curve. The rotation numbers and timbre have been defined as an internal invariant with respect to the flow.

Key words: nonwandering set, indecomposable continuum (atom), lakes of Wada (Wada basins), Birchoff’s curve, Euler characteristics, rotation number for the flow

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