论文信息 - Detection of all low-period windows for the logistic map

Detection of all low-period windows for the logistic map

A systematic method to find all low-period windows for the logistic map fa(x) = ax(1 - x) is proposed. The method is used to obtain very good approximations of positions of periodic windows with periods p ≤ 20. For each window using the forward shooting based interval Newton operator we confirm its existence by proving the existence of a sink for several parameter values inside the window and compute a very accurate rigorous lower bound of the window width.

Zbigniew Galias | Bartlomiej Garda

[1] Zbigniew Galias,et al. On the structure of existence regions for sinks of the Hénon map. , 2014, Chaos.

[2] Mikhail Lyubich. Almost every real quadratic map is either regular or stochastic , 1997 .

[3] Hüseyin Koçak,et al. SHADOWING IN DISCRETE DYNAMICAL SYSTEMS , 1996 .

[4] A. Neumaier. Interval methods for systems of equations , 1990 .

[5] Warwick Tucker,et al. A rigorous lower bound for the stability regions of the quadratic map , 2009 .

[6] Robert M. May,et al. Simple mathematical models with very complicated dynamics , 1976, Nature.

[7] Zbigniew Galias. Proving the existence of long periodic orbits in 1D maps using interval Newton method and backward shooting , 2002 .

[8] Konstantin Mischaikow,et al. Quantitative hyperbolicity estimates in one-dimensional dynamics , 2008 .