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Critically Finite Random Maps of an Interval. (arXiv:1810.05013v1 [math.DS])
来源于:arXiv
We consider random multimodal $C^3$ maps with negative Schwarzian derivative,
defined on a finite union of closed intervals in $[0,1]$, onto the interval
$[0,1]$ with the base space $\Omega$ and a base invertible ergodic map
$\theta:\Omega\to\Omega$ preserving a probability measure $m$ on $\Omega$. We
denote the corresponding skew product map by $T$ and call it a critically
finite random map of an interval. We prove that there exists a subset $AA(T)$
of $[0,1]$ with the following properties:
(1) For each $t\in AA(T)$ a $t$-conformal random measure $\nu_t$ exists. We
denote by $\lambda_{t,\nu_t,\omega}$ the corresponding generalized eigenvalues
of the corresponding dual operators $\mathcal{L}_{t,\omega}^*$,
$\omega\in\Omega$.
(2) Given $t\ge 0$ any two $t$-conformal random measures are equivalent.
(3) The expected topological pressure of the parameter $t$:
$$\mathcal{E}P(t):=\int_{\Omega}\log\lambda_{t,\nu,\omega}dm(\omega) $$ is
independent of the choice of a $t$-conformal random measu 查看全文>>