动力学(音乐)
统计物理学
计算机科学
数理经济学
数学
物理
声学
作者
Jack K. Hale,Hüseyin Koçak
出处
期刊:Springer eBooks
[Springer Nature]
日期:1991-01-01
被引量:990
标识
DOI:10.1007/978-1-4612-4426-4
摘要
This study presents ideas and examples about the geometry of dynamics and bifurcations of ordinary differential equations. The subject of differential and difference equations is an old and much-honoured chapter in science. In recent years, due primarily to the proliferation of computers, dynamical systems have returned to their roots in applications. It is the aim of this book to provide a modest foundation of knowledge for undergraduate and beginning graduate students in mathematics or science and engineering. Equations in dimension one and two constitute the majority of the text. It is demonstrated in particular that the basic notion of stability and bifurcations of vector fields are easily explained for scalar autonomous equations. Proceeding, the authors investigate the dynamics of planar autonomous equations where new dynamical behaviour, such as periodic and homoclinic orbits, appears.
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