Open Conformal Systems and Perturbations of Transfer Operators by Mark Pollicott & Mariusz Urbański

Author:Mark Pollicott & Mariusz Urbański
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

where, in general,

is the annulus centered at z with the inner radius r and the outer radius R; in order not to overlook a possible cases of negative numbers r − μ(B(x, r)) β , we naturally declare B(z, r) to be the empty set if r ≤ 0. We say that the measure μ is weakly boundary thin (WBT) with exponent β at the point x if

We simply say that measure μ is weakly boundary thin (WBT) at x if it is weakly boundary thin with some exponent β > 0. Given α > 0, we further define:

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