Refine
Year of publication
Document Type
- Article (4200)
- Doctoral Thesis (782)
- Postprint (137)
- Monograph/Edited Volume (120)
- Other (84)
- Preprint (44)
- Review (35)
- Habilitation Thesis (24)
- Conference Proceeding (15)
- Master's Thesis (11)
Keywords
- diffusion (58)
- stars: massive (56)
- gamma rays: general (47)
- anomalous diffusion (45)
- stars: early-type (45)
- cosmic rays (43)
- stars: winds, outflows (42)
- Magellanic Clouds (39)
- radiation mechanisms: non-thermal (38)
- X-rays: stars (37)
Institute
- Institut für Physik und Astronomie (5455) (remove)
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.