Talk:Dynamical system (definition)

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Contents 1 Creation 2 The claim 3 A new section 4 Definition of I(x) 5 T doesn't have to be a monoid 6 The term 7 WikiProject class rating

[edit] Creation

I have created this article from the definitions that were added to the Dynamical system page. I modified the definitions of the smooth cases to use a manifold as the state space. I also moved Linas' measure theoretic definition to this page. — XaosBits 20:11, 15 October 2006 (UTC)

[edit] The claim

The claim that cellular automata are not dynamical systems because they are not invertible is a contentious one. Dynamical systems need not be invertible, although some of them are. See, e.g. "Introduction to the Modern Theory of Dynamical Systems" by Katok & Hasselblatt, Chapter 0, p2:

For a reversible system the transformations phi_t are defined for both positive and negative values of t and each phi_t is invertible. (My emphasis)

- i.e. dynamical systems, including cellular automata, need not be reversible. 139.184.30.17 16:48, 19 October 2006 (UTC)

[edit] A new section

I would like to add a section to show how a evolution function could be constructed, with particular emphasis on the physical origins of the concept and its relations to engineering applications. Is there any problem? Any criticism is welcome. :) Daniele Tampieri 11:45, 26 November 2006

[edit] Definition of I(x)

193.204.253.144 14:10, 16 January 2007 (UTC)The current definition of I(x) is not very meaningful. , as is comprised of all the possible pairs in which the first element is in T and the second in M, so basically couldn't we simply write that I(x): = T?

[edit] T doesn't have to be a monoid

The restriction that T must be a monoid strikes any kind of incomplete flow. For example, dx / dt = x² is (by this definition) not a dynamical system, since it blows up in finite time. The space T depends on each initial condition. SmaleDuffin 19:06, 20 April 2007 (UTC)

I changed the general definition to include incomplete flows. SmaleDuffin 17:44, 24 April 2007 (UTC

[edit] The term

The term "Dynamical systems" is not correct English. It seems to be a translation from another language. Traditionally the terms are "static" and "dynamic". "Dynamical" doesn't make any more sense than "statical".

A search of Amazon does show books with "dynamical systems" in the title -- about 900 of them. However, there are about 3,000 titles with "dynamic systems" in them. So that's about a 10 to 3 vote for "Dynamic systems" over "Dynamical".

Romeo and Juliette was not a "Romantical Tragedy", either. - EI 208.34.100.161 03:06, 2 November 2007 (UTC)

Dynamical system is the term as used by mathematicians; see the American Mathematical Society Mathematics Subject Classification: http://www.ams.org/msc/. 37-xx is "Dynamical Systems and Ergodic Theory."

SmaleDuffin 18:11, 2 November 2007 (UTC)

[edit] WikiProject class rating

This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 09:48, 10 November 2007 (UTC)