Orbit of a point in Dynamical Systems

March 30, 2016

Abstract:

In this paper, we have proved the necessary and sufficient condition for a weakly mixing and topologically mixing function. Some properties of the monoid, periodic points and eventually periodic points are obtained. Some relations between weakly mixing, transitive and topologically mixing functions are obtained. Some results of considerable importance about the orbit of a point and relation with eventually periodic point are proved. Some results of the set theory that play an important role in our studies are included. Some new terms like singly transitive and lately transitive are introduced.

Author(s):

Babu Lal, Department of Applied Sciences, JCDM College of Engineering, Barnala Road, Sirsa (formerly HOD Department of Applied Sciences, JCDM COE, Sirsa)
Aseem Miglani, Registrar and Chairperson, Department of Mathematics, CDLU, Sirsa
Vinod Kumar, Visiting Professor, centre for advanced study in Mathematics, P.U. Chandigarh (formerly HOD Mathematics, K.U. Kurukshetra)

DOI:

https://doi.org/10.15415/mjis.2016.42012

Keywords:

Orbit, Eventually periodic point, Monoid, Dynamical system, Transitive, Weakly mixing

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