Attractor Dimension Estimates for Dynamical Systems: Theory and Computation: Dedicated to Gennady Leonov
暫譯: 動態系統的吸引子維度估計:理論與計算:獻給 Gennady Leonov

Kuznetsov, Nikolay, Reitmann, Volker

  • 出版商: Springer
  • 出版日期: 2021-07-03
  • 售價: $9,750
  • 貴賓價: 9.5$9,263
  • 語言: 英文
  • 頁數: 545
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3030509893
  • ISBN-13: 9783030509897
  • 海外代購書籍(需單獨結帳)

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商品描述

This book provides analytical and numerical methods for the estimation of dimension characteristics (Hausdorff, Fractal, Carathéodory dimensions) for attractors and invariant sets of dynamical systems and cocycles generated by smooth differential equations or maps in finite-dimensional Euclidean spaces or on manifolds. It also discusses stability investigations using estimates based on Lyapunov functions and adapted metrics. Moreover, it introduces various types of Lyapunov dimensions of dynamical systems with respect to an invariant set, based on local, global and uniform Lyapunov exponents, and derives analytical formulas for the Lyapunov dimension of the attractors of the Hénon and Lorenz systems. Lastly, the book presents estimates of the topological entropy for general dynamical systems in metric spaces and estimates of the topological dimension for orbit closures of almost periodic solutions to differential equations.

商品描述(中文翻譯)

本書提供了用於估計動態系統的吸引子和不變集的維度特徵(Hausdorff、Fractal、Carathéodory 維度)的分析和數值方法,這些系統由平滑微分方程或映射生成,並存在於有限維歐幾里得空間或流形上。書中還討論了使用基於 Lyapunov 函數和適應度量的估計進行穩定性研究。此外,書中介紹了與不變集相關的動態系統的各種類型的 Lyapunov 維度,這些維度基於局部、全局和均勻的 Lyapunov 指數,並推導了 Hénon 和 Lorenz 系統的吸引子的 Lyapunov 維度的解析公式。最後,本書呈現了在度量空間中一般動態系統的拓撲熵的估計,以及對微分方程幾乎周期解的軌道閉包的拓撲維度的估計。