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Abstract: The strange sets which arise in deterministic low dimensional dynamical systems are analyzed in terms of (unstable) cycles and their eigenvalues. The general formalism of cycle expansions is introduced and its convergence discussed. 1 present address: Dipartimento di Fisica dell'Universit`a and I.N.F.N., Via Celoria 16, I-20133 Milano 2 Carlsberg Fellow 1 INTRODUCTION The goal of the present series of papers is development of a perturbation theory of the low-dimensional deterministic... (Update)
Context of citations to this paper: More
.... a link between the dynamics over these discrete sets and the statistics of their continuous counterpart (see [Ruelle 1978; Artuso et al. 1990; Artuso 1991] and references therein) The discretization introduced by round off is significantly more difficult to deal with. In...
.... Gamma f Gamma1 (y) OE(x) X x:f(x) y OE(x) 1) for the time being we assume that f is a 1 dimensional map) A variety of applications [14, 12], some of which we shall turn to below, requires use of generalized transfer operators weighted by integer powers of the stability...
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2: Thermodynamic formalism (context) - Ruelle - 1978
2: Recycling of strange sets II: Applications - Artuso, Aurell et al. - 1990
BibTeX entry: (Update)
R. Artuso, E. Aurell, and P. Cvitanovi'c, "Recycling strange sets: I. Cycle expansions", Nonlinearity 3 (1990), 325--359. http://citeseer.ist.psu.edu/artuso90recycling.html More
@article{ artuso90recycling,
author = "R. Artuso and E. Aurell and P. Cvitanovic",
title = "Recycling of strange sets: {I}. Cycle expansions",
journal = "Nonlinearity",
volume = "3",
pages = "325--359",
year = "1990",
url = "citeseer.ist.psu.edu/artuso90recycling.html" }
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144 Thermodynamic Formalism (context) - Ruelle, Mechanics - 1978
41 Spectra of Graphs (context) - Cvetkovi'c, Doob et al. - 1980
28 Elements of Differentiable Dynamics and Bifurcation Theory (context) - Ruelle - 1989
21 Les m'ethodes nouvelles de la m'echanique c'eleste (context) - Poincar'e
11 Gunaratne and (context) - Cvitanovi'c - 1988
11 Hamiltonian Dynamical Systems (context) - MacKay, Miess - 1987
10 Procaccia and B (context) - Halsey, Jensen et al. - 1986
9 Ott and J (context) - Grebogi - 1987
8 Grebogi and J (context) - Ott - 1989
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6 Russian Math (context) - Pesin, Mat - 1977
6 Bell System Technical Journal (context) - Shannon - 1948
6 Eckhardt and P (context) - Cvitanovi'c
5 Inventiones math (context) - Ruelle - 1976
5 Cvitanovi'c and B (context) - Artuso - 1989
4 Dynamical Systems and Bifurcations of Vector Fields (context) - example, Guckenheimer et al. - 1986
4 submitted to Phys (context) - Christiansen, Paladin et al. - 1990
3 submitted to Phys (context) - Aurell, preprint
3 submitted to Nonlinearity (context) - Cvitanovi'c, Gunaratne et al.
1 Badii and A. P (context) - Politi, Badii et al. - 1988
1 to appear (context) - Aurell, Stat
1 for their evaluation for maps of the interval (context) - were, in et al. - 1965
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