# BOUNDS OF CORRELATION DIMENSIONS FOR SNAPSHOT ATTRACTORS

• Chang, Sung-Kag (Department of Mathematics, Yeungnam University) ;
• Lee, Mi-Ryeong (Department of Mathematics, Kyung-pook National University) ;
• Lee, Hung-Hwan (Department of Mathematics, Kyung-pook National University)
• Published : 2004.05.01

#### Abstract

In this paper, we reformulate a snapshot attractor([5]), ($K,\;\={\mu_{\iota}}$) generated by a random baker's map with a sequence of probability measures {\={\mu_{\iota}}} on K. We obtain bounds of the correlation dimensions of ($K,\;\={\mu_{\iota}}$) for all ${\iota}\;{\geq}\;1$.

#### References

1. Phys. v.D8 no.3 The infinite number of generalized dimensions of fractals and strange attractors H.G.E.Hentschel;I.Procaccia
2. Chaos in dynamical systems E.Ott
3. Phys. Rev. v.E53 no.3 Fractal dimension fluctuations for snapshot attractors of random maps A.Mamenson;E.Ott;T.M.Antonsen
4. Comm. Math. Phys. v.117 no.4 Dimension formula for random transformations F.Ledrappier;L.S.Young https://doi.org/10.1007/BF01218383
5. Ergodic Theory Dynam. Systems v.17 no.4 Are the diemesions of a set and its images equal under typical smooth functions T.D.Sauer;J.A.Yorke https://doi.org/10.1017/S0143385797086252
6. Ergodic theory and information P.Billingsley
7. Phys. Rev. Lett. v.50 no.5 Characterization of strange attractros P.Grassberger;I.Procaccia https://doi.org/10.1103/PhysRevLett.50.346
8. Phys. Rev. Lett. v.65 Transition to chaos for random dynamical systmes L.Yu;E.Ott;Q.Chen https://doi.org/10.1103/PhysRevLett.65.2935
9. J. Statist. Phys. v.71 no.3-4 On rigorous definition of correlation dimension and generalized spectrum for dimensions Y.Pesin https://doi.org/10.1007/BF01058436

#### Cited by

1. THE CORRELATION DIMENSION OF GENERALIZED CANTOR-LIKE SETS vol.34, pp.2, 2012, https://doi.org/10.5831/HMJ.2012.34.2.219