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The Analysis of Quasi-Continuous Functions
We give examples of quasi-continuous functions whose second iterates are discontinuous everywhere in the domain. A function is quasi-continuous if the inverse image of every open set in the codomain is quasi-open in the ...
Dynamics of Piecewise Continuous Functions
In our paper, we explore the chaotic behavior of a class of piecewise continuous functions defined on an interval X in the real line. A function or curve is piecewise continuous if it is continuous at all but a finite ...
Closed Geodesics on the Punctured Torus
We examine the behavior of geodesics on the punctured torus. We first consider simple geodesics and the results of . In particular, it can be shown that the lifts of these geodesics into the upper half plane are ...