Additive dimension theory for birkhoff curves

Alexander V. Osipov, Ivan A. Kovalew, Dmitry W. Serow

Research output


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 languageEnglish
Pages (from-to)164-176
Number of pages13
JournalNonlinear Phenomena in Complex Systems
Issue number2
Publication statusPublished - 2018

Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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