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Invariant densities for C¹ maps

100%

N. Quas A.

Studia Mathematica

1996

tom 120

nr 1

83-88

We consider the set of $C^1$ expanding maps of the circle which have a unique absolutely continuous invariant probability measure whose density is unbounded, and show that this set is dense in the space of $C^1$ expanding maps with the $C^1$ topology. This is in contrast with results for $C^2$ or $C^{1+ε}$ maps, where the invariant densities can be shown to be continuous.

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On continuous time version of two-phase cell cycle model of Tyrcha

100%

Zwoleński P.

Mathematica Applicanda

2013

tom 41

nr 1

We consider a model of two-phase cell cycle in a maturity-structured cellular population, which consists of a system of first order linear partial differential equations (transport equations). The model is based on similar biological assumptions as models of Lasota-Mackey, Tyson-Hannsgen and Tyrcha. We examine behavior of the solutions of the system along characteristics, give conditions for existence of invariant density, and compare results with outcomes of generational model.

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1 Mathematica Applicanda

1 Studia Mathematica

1 N. Quas A.

1 Zwoleński P.

1 2013

1 1996

Wyniki wyszukiwania

Invariant densities for C¹ maps

On continuous time version of two-phase cell cycle model of Tyrcha