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Prog. Theor. Phys. Vol. 80 No. 5 (1988) pp. 809-826

[ Full Text PDF : FREE ACCESS (892K) ]

Characterization of Local Structures of Chaotic Attractors in Terms of Coarse-Grained Local Expansion Rates

Hiroki Hata, Takehiko Horita, Hazime Mori, Terumitsu Morita and Koji Tomita

Department of Physics, Kyushu University 33, Fukuoka 812

(Received March 2, 1988)

Abstract:

Chaotic attractors at the bifurcation points of band mergings (or splittings), crises and saddlenode bifurcations have singular local structures which produce coherent large fluctuations of the coarse-grained local expansion rates of nearby orbits. Such local structures are studied in terms of a weighted average Λ(q), (-∞<q<∞) of the coarse-grained local expansion rates along the local unstable manifold with a q-dependent weight. By taking invertible two-dimensional and noninvertible one-dimensional maps, it is shown that, as q is varied, Λ(q) exhibits discontinuous phase transitions at discrete values of q;qα, qβ,…. Three types of such phase transitions are discussed. One is that caused by the homoclinic tangencies with qα=2.0. The second is that due to the accumulation of homoclinic tangency points at unstable periodic points with qβ≃-0.8. The third is that due to the intermittent hopping motions between two repellers with qγ=1.0. Different phases of the phase transitions represent different local structures. Thus the q-weighted average Λ(q) turns out to provide a useful means for characterizing singular local structures of chaotic attractors.


URL : http://ptp.ipap.jp/link?PTP/80/809/
DOI : 10.1143/PTP.80.809

[ Full Text PDF : FREE ACCESS (892K) ] Citation:

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  18. Progress of Theoretical Physics Supplement No.99 (1989) pp. 1-63 :
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