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商品描述
There is an explosion of interest in dynamical systems in the mathematical community as well as in many areas of science. The results have been truly exciting: systems which once seemed completely intractable from an analytic point of view can now be understood in a geometric or qualitative sense rather easily.
Scientists and engineers realize the power and the beauty of the geometric and qualitative techniques. These techniques apply to a number of important nonlinear problems ranging from physics and chemistry to ecology and economics.
Computer graphics have allowed us to view the dynamical behavior geometrically. The appearance of incredibly beautiful and intricate objects such as the Mandelbrot set, the Julia set, and other fractals have really piqued interest in the field.
This is text is aimed primarily at advanced undergraduate and beginning graduate students. Throughout, the author emphasizes the mathematical aspects of the theory of discrete dynamical systems, not the many and diverse applications of this theory.
The field of dynamical systems and especially the study of chaotic systems has been hailed as one of the important breakthroughs in science in the past century and its importance continues to expand. There is no question that the field is becoming more and more important in a variety of scientific disciplines.
New to this edition:
-Greatly expanded coverage complex dynamics now in Chapter 2
-The third chapter is now devoted to higher dimensional dynamical systems.
-Chapters 2 and 3 are independent of one another.
-New exercises have been added throughout.
商品描述(中文翻譯)
在數學社群以及許多科學領域中，對動態系統的興趣正在迅速增長。這些結果確實令人興奮：曾經從分析的角度看似完全無法處理的系統，現在可以相對輕鬆地以幾何或定性方式理解。
科學家和工程師意識到幾何和定性技術的力量與美感。這些技術適用於許多重要的非線性問題，涵蓋物理學、化學、生態學和經濟學等領域。
計算機圖形學使我們能夠以幾何方式觀察動態行為。像曼德布羅特集（Mandelbrot set）、朱利亞集（Julia set）和其他分形等令人驚嘆且複雜的物體的出現，確實激發了人們對這一領域的興趣。
本書主要針對高年級本科生和初級研究生。全書中，作者強調離散動態系統理論的數學方面，而非該理論的眾多和多樣的應用。
動態系統領域，特別是混沌系統的研究，被譽為過去一個世紀科學的重要突破之一，其重要性仍在不斷擴大。毫無疑問，這一領域在各種科學學科中的重要性日益增加。
本版新增內容：
- 第二章大幅擴展了複雜動力學的涵蓋範圍
- 第三章現在專門討論高維動態系統
- 第二章和第三章彼此獨立
- 全書新增了練習題
作者簡介
Robert L. Devaney is currently Professor of Mathematics at Boston University. He received his PhD from the University of California at Berkeley in under the direction of Stephen Smale. He taught at Northwestern University and Tufts University before coming to Boston University in 1980. His main area of research is dynamical systems, primarily complex analytic dynamics, but also including more general ideas about chaotic dynamical systems. Lately, he has become intrigued with the incredibly rich topological aspects of dynamics, including such things as indecomposable continua, Sierpinski curves, and Cantor bouquets. He is also the author of A First Course in Chaotic Dynamical Systems, Second Edition, published by CRC Press.
作者簡介(中文翻譯)
羅伯特·L·德凡尼（Robert L. Devaney）目前是波士頓大學的數學教授。他在加州大學伯克利分校獲得博士學位，指導教授為史蒂芬·斯梅爾（Stephen Smale）。在1980年來到波士頓大學之前，他曾在西北大學和塔夫茨大學任教。他的主要研究領域是動態系統，主要集中在複雜解析動態學，但也包括對混沌動態系統的更一般性思考。最近，他對動態學中極其豐富的拓撲特性產生了興趣，包括不可分解的連通體、謝爾賓斯基曲線（Sierpinski curves）和康托花束（Cantor bouquets）等。他也是《混沌動態系統入門》（A First Course in Chaotic Dynamical Systems）第二版的作者，該書由CRC Press出版。
