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Dimension of measures invariant with respect to the Wa?ewska partial differential equation |
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| Authors: | Andrzej Lasota Tomasz Szarek |
| Affiliation: | a Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland b Institute of Mathematics, Polish Academy of Sciences, Bankowa 14, 40-007 Katowice, Poland |
| Abstract: | We study asymptotic properties of a nonlinear first-order partial differential equation which describes the reproduction of blood cells. This equation under conditions proposed by Wa?ewska generates a semigroup of transformations with highly chaotic behaviour of trajectories. We show that this semigroup has invariant measures with arbitrary large dimension. |
| Keywords: | First-order partial differential equation Semigroup of operators Invariant measure Dimension of measures |
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