Mutual singularities of overlapping attractor and repeller
- 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.
| Author details: | Vladimir ChigarevORCiD, Alexey KazakovORCiD, Arkadij PikovskijORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1063/5.0056891 |
| ISSN: | 1054-1500 |
| ISSN: | 1089-7682 |
| Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/34470236 |
| Title of parent work (English): | Chaos : an interdisciplinary journal of nonlinear science |
| Publisher: | American Institute of Physics |
| Place of publishing: | Melville |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2021/08/11 |
| Publication year: | 2021 |
| Release date: | 2024/07/11 |
| Volume: | 31 |
| Issue: | 8 |
| Article number: | 083127 |
| Number of pages: | 10 |
| Funding institution: | RSF Russian Science Foundation (RSF) [17-11-01041]; Laboratory of Dynamical Systems and Applications NRU HSE of the Russian Ministry of Science and Higher Education [075-15-20191931]; Ministry of Science and Higher Education of Russian Federation [0729-2020-0036] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
| Peer review: | Referiert |
