Convergence Speeds of Iterations of Ruelle Operator with Weakly Contractive IFS
نویسنده
چکیده
In [2] Fan and Pollicott gave an estimate of convergence speed of the iterations fSn g fgn=1 ( Sg being the Ruelle operator de ̄ned by a normalized summable variation potential function g on a subshift of ̄nite type.) Later on Fan and Jiang [1] extended it to locally expansive Dini dynamical system. It is known that the systems they considered have the bounded distortion property (BDP). We extend their results to weakly contractive Dini iterated function systems (X; fwjgj=1; fpjgj=1) which allow to have overlapping but may not have the BDP.
منابع مشابه
Ruelle Operator for Infinite Conformal Ifs
Let (X, {wj} m j=1, {pj} m j=1) (2 ≤ m < ∞) be a contractive iterated function system (IFS), where X is a compact subset of R. It is well known that there exists a unique nonempty compact set K such that K = ⋃m j=1 wj(K). Moreover, the Ruelle operator on C(K) determined by the IFS (X, {wj} m j=1, {pj} m j=1) (2 ≤ m < ∞) has been introduced in [FL]. In the present paper, the Ruelle operators det...
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