The purpose of these notes is to give a brief overview of some of the basic ideas involved in studying the breakdown of stability in finite dimensional dynamical systems. We will at the end arrive at one frontier of modern research: the problem of determining how 'chaotic' invariant sets can come into existence in such dynamical systems. We emphasize the relation between chaotic properties and hyperbolicity in dynamical systems.
Loss of stability and emergence of chaos in dynamical systems / R. Johnson. - In: JOURNAL OF ECONOMIC BEHAVIOR & ORGANIZATION. - ISSN 0167-2681. - STAMPA. - 16:(1991), pp. 93-113. [10.1016/0167-2681(91)90045-Y]
Loss of stability and emergence of chaos in dynamical systems
JOHNSON, RUSSELL ALLAN
1991
Abstract
The purpose of these notes is to give a brief overview of some of the basic ideas involved in studying the breakdown of stability in finite dimensional dynamical systems. We will at the end arrive at one frontier of modern research: the problem of determining how 'chaotic' invariant sets can come into existence in such dynamical systems. We emphasize the relation between chaotic properties and hyperbolicity in dynamical systems.
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