Random topological degree and random differential inclusions

Jan Andres, Lech Górniewicz


We present a random topological degree effectively applicable mainly to
periodic problems for random differential inclusions.
These problems can be transformed to the existence problems of random fixed points or
periodic orbits of the associated Poincaré translation operators. The solvability
can be so guaranteed either directly by means of nontrivial topological invariants
(random degree, index of a random direct potential) or via a randomization scheme using
deterministic results which are ``periodicity stable'' under implemented parameter values.


Random degree; random differential inclusions; random operators; random fixed points; random periodic orbits; transformation to the deterministic case; randomization scheme

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