Chaos, Fractals, and Noise
Chaos, Fractals, and Noise
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DOI：
10.1007/978-1-4612-4286-4
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
A. Lasota;M. Mackey
中科院分区：
文献类型：
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作者：
A. Lasota;M. Mackey
这本书的第一版最初出版于1985年，标题为“确定性系统的概率性质”。在这期间的几年里，人们对所谓的“混沌”系统的兴趣有增无减，但对应用的关注更加深思熟虑和清醒，这与数学领域的情况相符。应用科学家对非线性动力学的概念和技术的认真使用的兴趣，可能更多地是受到廉价计算机的可用性的刺激，而不是受到任何其他因素的刺激。因此，计算机实验一直是突出的，这表明可能存在于非线性系统中的现象的财富。特别是，它们允许人们观察这些系统的确定性和概率属性之间的相互依赖性，例如存在不变的措施和密度，统计稳定性和周期性，随机扰动的影响，吸引子的形成，以及许多其他。这本书的目的，特别是这第二版，是目前最新的理论方法，使人们能够研究这些影响。我们在第二版中不仅纠正了第一版的错误，而且还在五个部分和一个新的章节中添加了大量新材料。
The first edition of this book was originally published in 1985 under the ti tle" Probabilistic Properties of Deterministic Systems." In the intervening years, interest in so-called" chaotic" systems has continued unabated but with a more thoughtful and sober eye toward applications, as befits a ma turing field. This interest in the serious usage of the concepts and techniques of nonlinear dynamics by applied scientists has probably been spurred more by the availability of inexpensive computers than by any other factor. Thus, computer experiments have been prominent, suggesting the wealth of phe nomena that may be resident in nonlinear systems. In particular, they allow one to observe the interdependence between the deterministic and probabilistic properties of these systems such as the existence of invariant measures and densities, statistical stability and periodicity, the influence of stochastic perturbations, the formation of attractors, and many others. The aim of the book, and especially of this second edition, is to present recent theoretical methods which allow one to study these effects. We have taken the opportunity in this second edition to not only correct the errors of the first edition, but also to add substantially new material in five sections and a new chapter.