Abstract
Using rigorous numerical methods, we validate a part of the bifurcation diagram for a Poincaré map of the Rössler system (Rössler in Phys. Lett. A 57(5):397–398, 1976)—the existence of two period-doubling bifurcations and the existence of a branch of period two points connecting them. Our approach is based on the Lyapunov–Schmidt reduction and uses the C r-Lohner algorithm (Wilczak and Zgliczyński, available at http://www.ii.uj.edu.pl/~wilczak) to obtain rigorous bounds for the Rössler system.
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Communicated by Konstantin Mischaikow.
Research of D. Wilczak was supported by an annual national scholarship for young scientists from the Foundation for Polish Science.
Research of P. Zgliczyński was supported in part by Polish State Ministry of Science and Information Technology grant N201 024 31/2163.
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Wilczak, D., Zgliczyński, P. Period Doubling in the Rössler System—A Computer Assisted Proof. Found Comput Math 9, 611–649 (2009). https://doi.org/10.1007/s10208-009-9040-x
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DOI: https://doi.org/10.1007/s10208-009-9040-x