Hyperbolicity, stability and monodromy of dynamical systems

We propose a rigorous computational method for proving uniform hyperbolicity of dynamical systems. Besides finding structurally stable parameters, the algorithm can also be applied for the computation of the monodromy of dynamical systems. With this algorithm, we prove that the topology of the 2‐dim...

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Veröffentlicht in:	Proceedings in applied mathematics and mechanics 2007-12, Vol.7 (1), p.1030101-1030102
1. Verfasser:	Arai, Zin
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Sprache:	eng
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description	We propose a rigorous computational method for proving uniform hyperbolicity of dynamical systems. Besides finding structurally stable parameters, the algorithm can also be applied for the computation of the monodromy of dynamical systems. With this algorithm, we prove that the topology of the 2‐dimensional generalization of the Mandelbrot set is totally different from that of the original Mandelbrot set. Furthermore, we show that the monodromy of the complex Hénon map can be used to determine the dynamics of the real Hénon map. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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title	Hyperbolicity, stability and monodromy of dynamical systems
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