Time dependent Volterra integral inclusions in Banach spaces
Sergiu Aizicovici Yimin Ding N. S. Papageorgiou
Discrete & Continuous Dynamical Systems - A 1996, 2(1): 53-63 doi: 10.3934/dcds.1996.2.53
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.
keywords: Volterra integral inclusion compact evolution operator $m$-accretive operator mild (integral) solution.
Renormalization and $\alpha$-limit set for expanding Lorenz maps
Yiming Ding
Discrete & Continuous Dynamical Systems - A 2011, 29(3): 979-999 doi: 10.3934/dcds.2011.29.979
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.
keywords: Expanding Lorenz map $\alpha$-limit set. renormalization

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