Geography of Order and Chaos in Mechanics: Investigations of Quasi-Integrable Systems with Analytical, Numerical, and Graphical Tools

Cordani, Bruno

  • 出版商: Birkhauser Boston
  • 出版日期: 2024-09-05
  • 售價: $7,660
  • 貴賓價: 9.5$7,277
  • 語言: 英文
  • 頁數: 395
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031722256
  • ISBN-13: 9783031722257
  • 無法訂購

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商品描述

This monograph explores the dynamics in the particular but very important and significant case of quasi-integrable Hamiltonian systems, or integrable systems slightly perturbed by other forces. With both analytic and numerical methods, the book studies several of these systems - such as the hydrogen atom and the solar system, with the associated Arnold web - through modern tools such as the frequency-modified Fourier transform, wavelets, and the frequency-modulation indicator. Meanwhile, it draws heavily on the more standard KAM and Nekhoroshev theorems.

Geography of Order and Chaos in Mechanics contains many figures that illuminate its concepts in novel ways, but perhaps its most useful feature is its inclusion of software to reproduce the various numerical experiments. The graphical user interfaces of five supplied MATLAB programs allows readers without any knowledge of computer programming to visualize and experiment with the distribution of order, chaos and resonances in various Hamiltonian systems.

This monograph will be a valuable resource for professional researchers and certain advanced undergraduate students in mathematics and physics, as well as an exceptional reference for PhD students with an interest in perturbation theory.

The Second Edition includes a new chapter on theoretical and numerical results in the study of the solar system's (in)stability obtained since publication of the First Edition, clarifying the topological mechanism that causes the sudden increase in Mercury's eccentricity. An updated version of the companion software is also provided, which contains new features and better Graphical User Interfaces. Thanks to the compiled versions, all the software can be used even if the user does not have access to a MATLAB installation.

商品描述(中文翻譯)

這本專著探討了準可積 Hamiltonian 系統的動態,這是一個特別但非常重要且顯著的案例,或是受到其他力量輕微擾動的可積系統。透過分析和數值方法,本書研究了幾個這類系統,例如氫原子和太陽系,並與相關的 Arnold 網絡一起,使用現代工具如頻率修正的傅立葉變換、小波和頻率調變指標。同時,它也大量引用了更為標準的 KAM 和 Nekhoroshev 定理。

《力學中的秩序與混沌地理》包含許多以新穎方式闡明其概念的圖形,但或許其最有用的特點是包含了軟體,以重現各種數值實驗。提供的五個 MATLAB 程式的圖形用戶介面使得沒有任何計算機程式設計知識的讀者也能夠可視化並實驗各種 Hamiltonian 系統中的秩序、混沌和共振的分佈。

這本專著將成為數學和物理領域專業研究人員及某些高年級本科生的寶貴資源,同時也是對於對擾動理論感興趣的博士生的卓越參考。

第二版新增了一章,介紹自第一版出版以來在太陽系(不)穩定性研究中獲得的理論和數值結果,澄清了導致水星偏心率突然增加的拓撲機制。還提供了更新版本的伴隨軟體,包含新功能和更好的圖形用戶介面。由於編譯版本的存在,即使用戶沒有訪問 MATLAB 安裝,所有軟體也都可以使用。