Nonlinear Phenomena in Complex Systems, 2018, Vol.21, No.4, pp.389

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2018, Vol.21, No.4, pp.389 - 394

Fractional Densities for the Wada Basins
Alexander V. Osipov and Dmitry W. Serow

The recently proposed quasi-harmonic approximation to wave functions of bound states Fractional density for basis zero Schnirelmann density has been defined. Definition of the fractional density is similar to the Hausdorff-Besicovitch dimension. The existence of the basis zero Schnirelmann density for every Wada basin (Wada ocean) earlier has been proved. This means every Wada basin/ocean are quite topologically characterized to be fractional density. Therefore all fractional densities are invariant with respect to a plane homeomorphism.

Key words: dissipative dynamic system, rotation number, Birkhoff curve, indecomposable continuum (atom), Wada basins, Schnirelmann density, additive basis, order of basis, fractional density

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