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DCDS

A nonlinear Volterra inclusion associated to a family of time-dependent $m$-accretive operators,
perturbed by a multifunction, is considered in a Banach space. Existence results
are established
for both nonconvex and convex valued perturbations.
The class of extremal solutions is also
investigated.

DCDS

We show that there is a bijection between the renormalizations and
proper completely invariant closed sets of expanding Lorenz map,
which enables us to distinguish periodic and non-periodic
renormalizations. Based on the properties of the periodic orbit with
minimal period, the minimal completely invariant closed set is
constructed. Topological characterizations of the renormalizations
and $\alpha$-limit sets are obtained via consecutive
renormalizations. Some properties of periodic renormalizations are
collected in Appendix.

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