12,045 research outputs found
On multi-transitivity with respect to a vector
A topological dynamical system is said to be multi-transitive if for
every the system is transitive. We introduce the concept of multi-transitivity with
respect to a vector and show that multi-transitivity can be characterized by
the hitting time sets of open sets, answering a question proposed by Kwietniak
and Oprocha [On weak mixing, minimality and weak disjointness of all iterates,
Erg. Th. Dynam. Syst., 32 (2012), 1661--1672]. We also show that
multi-transitive systems are Li-Yorke chaotic.Comment: 11 page
Existence of translating solutions to the flow by powers of mean curvature on unbounded domains
In this paper, we prove the existence of classical solutions of the Dirichlet
problem for a class of quasi-linear elliptic equations on unbounded domains
like a cone or a U-type domain. This problem comes from the study of mean
curvature flow and its generalization, the flow by powers of mean curvature.
Our approach is a modified version of the classical Perron method, where the
solutions to the minimal surface equation are used as sub-solutions and a
family auxiliary functions are constructed as super-solutions.Comment: 30 page
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