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