Intermittency and Regularized Fredholm Determinants
| dc.creator | Rugh, Hans Henrik | |
| dc.date | 1996-10-07 | |
| dc.date.accessioned | 2026-07-07T09:07:58Z | |
| dc.date.available | 2026-07-07T09:07:58Z | |
| dc.description | We consider real-analytic maps of the interval $I=[0,1]$ which are expanding everywhere except for a neutral fixed point at 0. We show that on a certain function space the spectrum of the associated Perron-Frobenius operator ${\cal M}$ has a decomposition $Sp ({\cal M}) = σ_c \cup σ_p$ where $σ_c=[0,1]$ is the continuous spectrum of ${\cal M}$ and $σ_p$ is the pure point spectrum with no points of accumulation outside 0 and 1. We construct a regularized Fredholm determinant $d(λ)$ which has a holomorphic extension to $λ\in C-σ_c$ and can be analytically continued from each side of $σ_c$ to an open neighborhood of $σ_c-{0,1}$ (on different Riemann sheets). In $C-σ_c$ the zero-set of $d(λ)$ is in one-to-one correspondence with the point spectrum of ${\cal M}$. Through the conformal transformation $λ(z) = 1/(4z) (1+z)^2$ the function $d \circ λ(z)$ extends to a holomorphic function in a domain which contains the unit disc. | |
| dc.description | 22 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/chao-dyn/9610011 | |
| dc.identifier | http://arxiv.org/abs/chao-dyn/9610011 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150561 | |
| dc.subject | Chaotic Dynamics | |
| dc.title | Intermittency and Regularized Fredholm Determinants | |
| dc.type | text |