Xref: utzoo comp.theory.dynamic-sys:180 sci.math:15594 sci.physics:17278
Path: utzoo!news-server.csri.toronto.edu!rutgers!uwm.edu!caen!news.cs.indiana.edu!ariel.unm.edu!cie!scavo
From: scavo@cie.uoregon.edu (Tom Scavo)
Newsgroups: comp.theory.dynamic-sys,sci.math,sci.physics
Subject: Re: Intermittency
Keywords: mappings, intermittency, saddle-node bifurcation
Message-ID: <1991Mar07.165120.11462@ariel.unm.edu>
Date: 7 Mar 91 16:51:20 GMT
References: <1991Mar1.001103.6341@cec1.wustl.ed> <1991Mar6.232931.2553@agate.berkeley.edu>
Reply-To: scavo@cie.uoregon.edu (Tom Scavo)
Organization: University of Oregon Campus Information Exchange
Lines: 22

In article <1991Mar6.232931.2553@agate.berkeley.edu> william@ronzoni.berkeley.edu (W. E. Grosso) writes:
>I'm doing some research in dynamical systems for a paper 
>and presentation. The question : does anybody out there
>know about intermittency in dynamical systems 
>(from what I gather, it seems to be associated with 
>numerical experimentation).

Consider  E : R --> R  with  E(x) = \lambda exp(x) , for example. 
This map experiences a saddle-node bifurcation at  \lambda = 1/e.
Now, choose  \lambda  ever so slightly greater than  1/e  and
compute the orbit of  0 , say.  This orbit will eventually
"escape" to infinity, but only after many iterations;  E^n(0)
is said to be an _intermittent orbit_ for this value of  \lambda.

See section 6.8.1 in Guckenheimer & Holmes, _Nonlinear Oscil-
lations, Dynamical Systems, and Bifurcations of Vector Fields_,
Springer-Verlag, 1983.  See also Devaney's chapter in _The
Science of Fractal Images_, Springer-Verlag, 1988 (Peitgen &
Saupe, editors) on pp.163-167.

Tom Scavo
scavo@cie.uoregon.edu