### Abstract

Dyes of different colors advected by two-dimensional flaws which are asymptotically simple can form a fractal boundary that coincides with a chaotic saddle's unstable manifold. We show that such dye boundaries can have the Wada property: every boundary point of a given color on this fractal set is on the boundary of at feast two other colors. The condition for this is the nonempty intersection of the saddle's stable manifold with at least three differently colored domains in the asymptotic inflow region.

Original language | English |
---|---|

Pages (from-to) | 235-243 |

Number of pages | 9 |

Journal | Physica. A, Statistical Mechanics and its Applications |

Volume | 239 |

Issue number | 1-3 |

Publication status | Published - 1 May 1997 |

### Keywords

- leapfrogging vortex pairs
- scattering
- chaos

### Cite this

*Physica. A, Statistical Mechanics and its Applications*,

*239*(1-3), 235-243.

**Wada dye boundaries in open hydrodynamical flows.** / Toroczkai, Z ; Karolyi, G ; Pentek, A ; Tel, T ; Grebogi, C ; Yorke, J A .

Research output: Contribution to journal › Article

*Physica. A, Statistical Mechanics and its Applications*, vol. 239, no. 1-3, pp. 235-243.

}

TY - JOUR

T1 - Wada dye boundaries in open hydrodynamical flows

AU - Toroczkai, Z

AU - Karolyi, G

AU - Pentek, A

AU - Tel, T

AU - Grebogi, C

AU - Yorke, J A

PY - 1997/5/1

Y1 - 1997/5/1

N2 - Dyes of different colors advected by two-dimensional flaws which are asymptotically simple can form a fractal boundary that coincides with a chaotic saddle's unstable manifold. We show that such dye boundaries can have the Wada property: every boundary point of a given color on this fractal set is on the boundary of at feast two other colors. The condition for this is the nonempty intersection of the saddle's stable manifold with at least three differently colored domains in the asymptotic inflow region.

AB - Dyes of different colors advected by two-dimensional flaws which are asymptotically simple can form a fractal boundary that coincides with a chaotic saddle's unstable manifold. We show that such dye boundaries can have the Wada property: every boundary point of a given color on this fractal set is on the boundary of at feast two other colors. The condition for this is the nonempty intersection of the saddle's stable manifold with at least three differently colored domains in the asymptotic inflow region.

KW - leapfrogging vortex pairs

KW - scattering

KW - chaos

M3 - Article

VL - 239

SP - 235

EP - 243

JO - Physica. A, Statistical Mechanics and its Applications

JF - Physica. A, Statistical Mechanics and its Applications

SN - 0378-4371

IS - 1-3

ER -