Author:
FALCONER KENNETH J.,FRASER JONATHAN M.,LEE LAWRENCE D.
Abstract
AbstractWe study the
$L^{q}$
-spectrum of measures in the plane generated by certain nonlinear maps. In particular, we consider attractors of iterated function systems consisting of maps whose components are
$C^{1+\alpha }$
and for which the Jacobian is a lower triangular matrix at every point subject to a natural domination condition on the entries. We calculate the
$L^{q}$
-spectrum of Bernoulli measures supported on such sets by using an appropriately defined analogue of the singular value function and an appropriate pressure function.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献