DOI QR코드

DOI QR Code

CONTINUITY OF THE FRACTIONAL PART FUNCTION AND DYNAMICS OF CIRCLE

  • LAL, BABU (Department of Mathematics, Choudhary Devi Lal University) ;
  • MIGLANI, ASEEM (Department of Mathematics, Choudhary Devi Lal University) ;
  • SINGH, VIZENDER (Department of Mathematics, Directorate of Distance Education, GJUS&T)
  • Received : 2022.05.16
  • Accepted : 2022.07.19
  • Published : 2022.09.30

Abstract

In this paper, we obtain some subsets of real numbers (ℝ) on which a fractional part function is defined as a real-valued continuous function. This gives rise to the analysis of the continuous properties of the fractional part function as a real-valued function. The analysis of fractional part function is helpful in the study of the dynamics of circle.

Keywords

References

  1. B. Lal, A. Miglani and V. Kumar, On Dynamics of Circle Maps, Proceedings 2nd International Conference on Evolution in Science and Technology and Eyne on Educational Methodology, March 3-4, 2013, PPIMT, Hisar, 507-510.
  2. M. Brin and G. Stuck, Introduction to Dynamical Systems, Cambridge University Press, 2002.
  3. S. Gadgil, Dynamics on the circle 1, Resonance 8 (2003).
  4. P. Sharma and A. Nagar, On dynamics of circle maps, Far-East Journal of Dynamical Systems 10 (2008), 185-201.
  5. Q. Zhang, Invertible Circle Maps, Lecture (12) notes, Dynamical System 110(421).
  6. G.D. Birkhoff, Dynamical Systems, AMS Colloq. Publ., 9 1927, Collected mathematical papers, 3 1950.
  7. J.R. Munkres, Topology: A First Course, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1975.
  8. J.L. Kelley, General Topology, Van Nostrand, 1955.