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Re: Plot a simple function

• To: mathgroup at smc.vnet.net
• Subject: [mg74884] Re: Plot a simple function
• From: Roger Bagula <rlbagula at sbcglobal.net>
• Date: Tue, 10 Apr 2007 05:13:16 -0400 (EDT)
• References: <evab3s$d6b$1@smc.vnet.net> <evd4a2$6b3$1@smc.vnet.net>

There is yet another way to get this type of diagram!

http://arxiv.org/pdf/chao-dyn/9804006
Working on these diagrams jogged a memory:
look at figure 3 c) and d) in this paper.
He calls it the Igloo map as related to the Logistic map.


http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id==
CHAOEH000010000001000180000001&idtype=cvips&gifs=yes

Entropy computing via integration over fractal measures

Wojciech Slomczynski
Instytut Matematyki, Uniwersytet Jagiellonski, ul. Reymonta 4, 30=96059,
Krak=F3w, Poland

Jaroslaw Kwapien
Instytut Fizyki Jadrowej im. H. Niewodniczanskiego, ul. Radzikowskiego
152, 31=96305, Krak=F3w, Poland

Karol Zyczkowski
Instytut Fizyki im. M. Smoluchowskiego, Uniwersytet Jagiellonski, ul.
Reymonta 4, 30=96059, Krak=F3w, Poland

(Received 20 January 1999; accepted 10 August 1999)

We discuss the properties of invariant measures corresponding to
iterated function systems (IFSs) with place-dependent probabilities and
compute their R=E9nyi entropies, generalized dimensions, and multifractal
spectra. It is shown that with certain dynamical systems, one can
associate the corresponding IFSs in such a way that their generalized
entropies are equal. This provides a new method of computing entropy for
some classical and quantum dynamical systems. Numerical techniques are
based on integration over the fractal measures. =A92000 American Institute
of Physics.

PII: S1054-1500(99)01204-5
doi:10.1063/1.166492
PACS: 05.45.Df, 02.50.Cw, 02.60.Jh Additional Information