Pesin-Type Identity for Weak Chaos
| dc.creator | Korabel, Nickolay | |
| dc.creator | Barkai, Eli | |
| dc.date | 2008-08-10 | |
| dc.date.accessioned | 2026-07-07T12:37:27Z | |
| dc.date.available | 2026-07-07T12:37:27Z | |
| dc.description | Pesin's identity provides a profound connection between entropy $h_{KS}$ (statistical mechanics) and the Lyapunov exponent $λ$ (chaos theory). It is well known that many systems exhibit sub-exponential separation of nearby trajectories and then $λ=0$. In many cases such systems are non-ergodic and do not obey usual statistical mechanics. Here we investigate the non-ergodic phase of the Pomeau-Manneville map where separation of nearby trajectories follows $δx_t= δx_0 e^{λ_α t^α}$ with $0<α<1$. The limit distribution of $λ_α$ is the inverse L{é}vy function. The average $< λ_α >$ is related to the infinite invariant density, and most importantly to entropy. Our work gives a generalized Pesin's identity valid for systems with an infinite invariant density. | |
| dc.description | 5 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/0808.1398 | |
| dc.identifier | http://arxiv.org/abs/0808.1398 | |
| dc.identifier | Phys. Rev. Lett. 102, 050601 (2009) | |
| dc.identifier | doi:10.1103/PhysRevLett.102.050601 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/218446 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Other Condensed Matter | |
| dc.subject | Chaotic Dynamics | |
| dc.title | Pesin-Type Identity for Weak Chaos | |
| dc.type | text |