动力系统双曲性和结构稳定性的计算机测试

Q3 Mathematics

Differencialnie Uravnenia i Protsesy Upravlenia Pub Date : 2023-01-01 DOI:10.21638/11701/spbu35.2023.302

George Osipenko

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引用次数: 0

摘要

如果摩尔斯谱不含零，则在链循环集上的微分同态是双曲的。符号象是一个近似于动态系统的有向图。用这个图对链循环集进行了定域。微分信号的符号图像使我们能够估计摩尔斯谱。如果对偶微分只有平凡有界轨迹，则微分同态f是结构稳定的。对偶微分的符号象使得检查对偶微分是否存在有界轨迹成为可能。

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Computer-oriented Tests for Hyperbolicity and Structural Stability of Dynamical System

A diffeomorphism f is hyperbolic on a chain-recurrent set if the Morse spectrum does not contain zero. The symbolic image is a directed graph approximating a dynamical system. The chain-recurrent set is localized using this graph. The symbolic image of the differential allows us to estimate the Morse spectrum. A diffeomorphism f is structurally stable if the dual differential has only trivial bounded trajectories. The symbolic image of the dual differential makes it possible to check the absence of bounded trajectories of the dual differential.

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来源期刊

Differencialnie Uravnenia i Protsesy Upravlenia Mathematics-Analysis

CiteScore

1.10

自引率

0.00%

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