Article View: comp.theory.dynamic-sys
Article #137Re: Intermittency
From: Tom Scavo
Date: Thu, 07 Mar 1991 16:51
Date: Thu, 07 Mar 1991 16:51
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1657 bytes
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
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Path: arc1-ca.pugleaf.net!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