Piecewise linear maps with heterogeneous chaos
| Autor: | Hiroki Takahasi, Yoshitaka Saiki, James A. Yorke |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Dense set
Lebesgue measure Dynamical systems theory Applied Mathematics Ergodicity Chaotic FOS: Physical sciences General Physics and Astronomy Statistical and Nonlinear Physics Dynamical Systems (math.DS) Nonlinear Sciences - Chaotic Dynamics Nonlinear Sciences::Chaotic Dynamics Piecewise linear function FOS: Mathematics Ergodic theory Statistical physics Mathematics - Dynamical Systems Chaotic Dynamics (nlin.CD) Invariant (mathematics) Mathematical Physics Mathematics |
| Zdroj: | Nonlinearity. 34:5744-5761 |
| ISSN: | 1361-6544 0951-7715 |
| DOI: | 10.1088/1361-6544/ac0d45 |
| Popis: | Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic invariant set is heterogeneous when arbitrarily close to each point of the set there are different periodic points with different numbers of unstable dimensions. We call such dynamics heterogeneous chaos (or hetero-chaos), While we believe it is common for physical systems to be hetero-chaotic, few explicit examples have been proved to be hetero-chaotic. Here we present two more explicit dynamical systems that are particularly simple and tractable with computer. It will give more intuition as to how complex even simple systems can be. Our maps have one dense set of periodic points whose orbits are 1D unstable and another dense set of periodic points whose orbits are 2D unstable. Moreover, they are ergodic relative to the Lebesgue measure. Comment: 16 pages, 9 figures |
| Databáze: | OpenAIRE |
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