Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 29, pp. 43-49 (2013)

Chaotic behavior based on discontinuous maps

Molaei, M. R. and Karami, M.

Shahid Bahonar University of Kerman

Abstract: In this paper a class of chaotic vector fields in $R^{3}$ is considered. We prove its chaotic behavior by using of the topological entropy of a class of interval maps with finite number of discontinuities. Semi-Lorenz maps from the viewpoint of topological entropy are studied and it is proved that they have positive topological entropies. A kind of bifurcation by presenting a class of one parameter families of interval maps is studied.

Keywords: Topological entropy; Interval maps; Semi-Lorenz map; Chaotic vector fields

Classification (MSC2000): 37B40; 37D45

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