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Dynamics of birth-and-death processes with proliferation - stability and chaos

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  • We provide a detailed description of long time dynamics in $l^1$ of the semigroup associated with constant coefficient infinite birth-and-death systems with proliferation. In particular, we discuss and slightly extend earlier stability results of [8] and also identify a range of parameters for which the semigroup is both stable in the sense of op. cit. and topologically chaotic. Moreover, for a range of parameters, we provide an explicit description of subspaces of $l^1$ which cannot generate chaotic orbits.
    Mathematics Subject Classification: 34G10, 37B99, 47A16, 47D03.


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