Jump to ContentJump to Main Navigation
Advanced MechanicsFrom Euler's Determinism to Arnold's Chaos$
Users without a subscription are not able to see the full content.
Advanced Mechanics: From Euler's Determinism to Arnold's Chaos

S. G. Rajeev

Print publication date: 2013

Print ISBN-13: 9780199670857

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199670857.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 23 October 2021

Dynamics in one real variable

Dynamics in one real variable

Chapter:
(p.125) 16 Dynamics in one real variable
Source:
Advanced Mechanics
Author(s):

S. G. Rajeev

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199670857.003.0016

Discrete time dynamics is simply the repeated action of the same function. Surprisingly, even the simplest case of the iteration of a function of one real variable can lead to chaos. This chapter introduces the idea of a fixed point, and its stability. Cobweb diagrams are used to visualize orbits. The doubling map is an example of chaos. Feigenbaum's period doubling approach to chaos is explained at an elementary level. Examples of invariance measures are given.

Keywords:   iteration, fixed point, stability, cobweb diagram, chaos, period doubling, invariance measures

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .