Article in magazine Chaos
Article of research assistant V.G. Chigarev, leading research fellow A.O. Kazakov and chief research fellow A. Pikovsky published in the journal "Chaos: An Interdisciplinary Journal of Nonlinear Science"
The article “The distance of Kantorovich – Rubinstein – Wasserstein between the overlapping attractor and repeller” was marked as “Editor's Pick”. Over the past two years, A. Pikovsky and A.O. Kazakov have published three articles that marked as an “Editor's Pick”. This highlights the relevance of the topic and the significance of the results of published research for the mathematical community.
Authors of the article: V.G. Chigarev, A.O. Kazakov and A. Pikovsky.
We consider several examples of dynamical systems demonstrating overlapping attractor and repeller. These systems are constructed via introducing controllable dissipation to prototypic models with chaotic dynamics (Anosov cat map, Chirikov standard map, and incompressible three-dimensional flow of the ABC-type on a three-torus) and ergodic non-chaotic behavior (skew-shift map). We employ the Kantorovich–Rubinstein–Wasserstein distance to characterize the difference between the attractor and the repeller, in dependence on the dissipation level.