Singular invariant measures on the line

We determine the asymptotic behaviour of the iterates of the Perron-Frobenius operator for specific interval maps with an indifferent fixed point which gives rise to an infinite invariant measure.

Two problems on doubling measures.

Robert Kaufman, Jang-Mei Wu (1995)

Revista Matemática Iberoamericana

Similarity:

Doubling measures appear in relation to quasiconformal mappings of the unit disk of the complex plane onto itself. Each such map determines a homeomorphism of the unit circle on itself, and the problem arises, which mappings f can occur as boundary mappings?

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