TY  - JOUR
A1  - Chigarev, Vladimir
A1  - Kazakov, Alexey
A1  - Pikovskij, Arkadij
T1  - Mutual singularities of overlapping attractor and repeller
T2  - Chaos : an interdisciplinary journal of nonlinear science
N2  - We apply the concepts of relative dimensions and mutual singularities to characterize the fractal properties of overlapping attractor and repeller in chaotic dynamical systems. We consider one analytically solvable example (a generalized baker's map); two other examples, the Anosov-Mobius and the Chirikov-Mobius maps, which possess fractal attractor and repeller on a two-dimensional torus, are explored numerically. We demonstrate that although for these maps the stable and unstable directions are not orthogonal to each other, the relative Renyi and Kullback-Leibler dimensions as well as the mutual singularity spectra for the attractor and repeller can be well approximated under orthogonality assumption of two fractals.
Y1  - 2021
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/64727
SN  - 1054-1500
SN  - 1089-7682
VL  - 31
IS  - 8
PB  - American Institute of Physics
CY  - Melville
ER  -