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Recombination semigroups on measure spaces. (English) Zbl 1081.92028
Monatsh. Math. 146, No. 4, 267-278 (2005); addendum ibid. 150, No. 1, 83-84 (2007).
Summary: The dynamics of recombination in genetics leads to an interesting nonlinear differential equation, which has a natural generalization to a measure valued version. The latter can be solved explicitly under rather general circumstances. It admits a closed formula for the semigroup of nonlinear positive operators that emerges from the forward flow and is, in general, embedded in a multi-parameter semigroup.

MSC:
92D10 Genetics and epigenetics
34L30 Nonlinear ordinary differential operators
34A34 Nonlinear ordinary differential equations and systems
34G99 Differential equations in abstract spaces
47H20 Semigroups of nonlinear operators
46N60 Applications of functional analysis in biology and other sciences
37N25 Dynamical systems in biology
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