Inverse Limits Associated with the Forced Van Der Pol Equation
In "Qualitative Analysis of the Periodically Forced Relaxation Oscillations," Mark Levi (Mem. Am. Math. Soc. 32, No. 244, July 1981) gives a nice geometric description of annulus maps associated with the first return map for the forced van der Pol equation εx+Φ(x)x+εx=bp(t). In this paper, it is shown that for certain parameter valuesb, the full attracting sets of the annulus maps described by Levi can be realized as inverse limits of circles. Furthermore, we show that the annulus map is topologically conjugate to the shift homeomorphism on the inverse limit space.
S. E. Holte and R. P. Roe, "Inverse Limits Associated with the Forced Van Der Pol Equation," Journal of Dynamics and Differential Equations, Springer Verlag, Jan 1994.
The definitive version is available at https://doi.org/10.1007/BF02218849
Mathematics and Statistics
Keywords and Phrases
Gvan der Pol equation; inverse limit space
Article - Journal
© 1994 Springer Verlag, All rights reserved.