Dawidowicz, Antoni Leon On invariant measures supported on compact sets. II. (English) Zbl 0795.28015 Zesz. Nauk. Uniw. Jagielloń. 991, Acta Math. 29, 25-28 (1992). 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. Cited in 1 Document 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 Keywords:differential equation of von Foerster type; invariant measure; dynamical system; stability Citations:Zbl 0616.28011; Zbl 0566.28013 PDFBibTeX XMLCite \textit{A. L. Dawidowicz}, Zesz. Nauk. Uniw. Jagielloń. [...], Acta Math. 991(29), 25--28 (1992; Zbl 0795.28015)