### Abstract

The additive dimension for a common boundary of the Wada basins bases (and Wada ocean) accessible points has been defined. One is constituted to be value being inverse to fractional density for the sequence (basis) zero Schnirelmann density and one characterizes only metric property of the boundary (Birkhoff curve). The additive dimension is similar to Hausdorff–Besicovitch dimension. All Wada basin and Wada ocean are quite metrically characterized to be only additive dimension of accessible points. It follows that additive dimension is invariant with respect to a plane diffeomorphism.

Original language | English |
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Pages (from-to) | 164-176 |

Number of pages | 13 |

Journal | Nonlinear Phenomena in Complex Systems |

Volume | 22 |

Issue number | 2 |

Publication status | Published - 2018 |

### Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Osipov, A. V., Kovalew, I. A., & Serow, D. W. (2018). Additive dimension theory for birkhoff curves.

*Nonlinear Phenomena in Complex Systems*,*22*(2), 164-176.