### Abstract

Recent studies have revealed that riddled fractal sets, sets whose conventionally defined fractal dimensions are integers; occur commonly in chaotic dynamical systems. We demonstrate that these exotic fractal sets exhibit a sign-singular scaling behavior with nontrivial scaling exponents. The exponents may then be used to characterize the sets. Numerical examples using both a low-dimensional map and a coupled map lattice are given.

Original language | English |
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Pages (from-to) | 1371-1374 |

Number of pages | 4 |

Journal | Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 53 |

Issue number | 2 |

Publication status | Published - Feb 1996 |

### Cite this

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*53*(2), 1371-1374.

**Characterizing riddled fractal sets.** / Lai, Y C ; Grebogi, C ; Lai, Ying-Cheng.

Research output: Contribution to journal › Article

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 53, no. 2, pp. 1371-1374.

}

TY - JOUR

T1 - Characterizing riddled fractal sets

AU - Lai, Y C

AU - Grebogi, C

AU - Lai, Ying-Cheng

PY - 1996/2

Y1 - 1996/2

N2 - Recent studies have revealed that riddled fractal sets, sets whose conventionally defined fractal dimensions are integers; occur commonly in chaotic dynamical systems. We demonstrate that these exotic fractal sets exhibit a sign-singular scaling behavior with nontrivial scaling exponents. The exponents may then be used to characterize the sets. Numerical examples using both a low-dimensional map and a coupled map lattice are given.

AB - Recent studies have revealed that riddled fractal sets, sets whose conventionally defined fractal dimensions are integers; occur commonly in chaotic dynamical systems. We demonstrate that these exotic fractal sets exhibit a sign-singular scaling behavior with nontrivial scaling exponents. The exponents may then be used to characterize the sets. Numerical examples using both a low-dimensional map and a coupled map lattice are given.

M3 - Article

VL - 53

SP - 1371

EP - 1374

JO - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 2

ER -