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Advanced MechanicsFrom Euler's Determinism to Arnold's Chaos$
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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

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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

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