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On invariant measures supported on compact sets. II. (English) Zbl 0795.28015

In the first part [Zesz. Nauk Univ. Jagielloń. 715, Pr. Mat. 25, 277- 283 (1985; Zbl 0616.28011)] the author considered the differential equation of von Foerster type with one-parametric characteristic of maturity. In the quoted paper the invariant measure for the dynamical system generated by this equation was constructed. A similar problem was considered by R. Rudnicki [Ergodic Theory Dyn. Syst. 5, 437-443 (1985; Zbl 0566.28013)] who obtained an invariant measure with better properties. However, his construction uses the fact that characteristic of maturity is one-dimensional. In the present paper the author proves that his result obtained in Part I is also true in the multidimensional case. This equation has been considered by K. Łoskot (to appear), who has examined its solution with regard to stability and turbulence in the sense of Bass.

MSC:

28D10 One-parameter continuous families of measure-preserving transformations
35F25 Initial value problems for nonlinear first-order PDEs
35B35 Stability in context of PDEs
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