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Pesin theory and equilibrium measures on the interval

100%

Dobbs N.

Fundamenta Mathematicae

2015

tom 231

nr 1

1-17

We use Pesin theory to study possible equilibrium measures for a broad class of piecewise monotone maps of the interval and a broad class of potentials.

Non-existence of absolutely continuous invariant probabilities for exponential maps

63%

Dobbs N., Skorulski B.

Fundamenta Mathematicae

2008

tom 198

nr 3

283-287

We show that for entire maps of the form z ↦ λexp(z) such that the orbit of zero is bounded and Lebesgue almost every point is transitive, no absolutely continuous invariant probability measure can exist. This answers a long-standing open problem.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Dobbs N.

1 Skorulski B.

1 2015

1 2008

Wyniki wyszukiwania

Pesin theory and equilibrium measures on the interval

Non-existence of absolutely continuous invariant probabilities for exponential maps