Dynamics of real projective transformations

Authors

  • Sharan Gopal Birla Institute of Technology and Science - Pilani
  • Srikanth Ravulapalli University of Hyderabad

DOI:

https://doi.org/10.4995/agt.2018.7962

Keywords:

topological entropy, zeta function, projective transformation

Abstract

The dynamics of a projective transformation on a real projective space are studied in this paper. The two main aspects of these transformations that are studied here are the topological entropy and the zeta function. Topological entropy is an inherent property of a dynamical system whereas the zeta function is a useful tool for the study of periodic points. We find the zeta function for a general projective transformation but entropy only for certain transformations on the real projective line.

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Author Biographies

Sharan Gopal, Birla Institute of Technology and Science - Pilani

Assistant Professor

Department of Mathematics

Srikanth Ravulapalli, University of Hyderabad

Research Scholar

School of Mathematics and Statistics

References

R. L. Adler, A. G. Konheim and M. H. McAndrew, Topological entropy, Transactions of the American Mathematical Society 114 (1965), 309-319. https://doi.org/10.1090/S0002-9947-1965-0175106-9

R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Transactions of the American Mathematical Society 153 (1971), 401-414. https://doi.org/10.1090/S0002-9947-1971-0274707-X

M. Brin and G. Stuck, Introduction to dynamical systems, Cambridge University Press (2004).

S. G. Dani, Dynamical properties of linear and projective transformations and their applications, Indian J. Pure Appl. Math. 35 (2004), 1365-1394.

R. Devaney, An introduction to chaotic dynamical systems, Second edition, Addison-Wesley Publishing Company Advanced Book Program, Redwood City, CA, 1989.

N. H. Kuiper, Topological conjugacy of real projective transformations, Topology 15 (1976), 13-22. https://doi.org/10.1016/0040-9383(76)90046-X

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Published

2018-10-04

How to Cite

[1]
S. Gopal and S. Ravulapalli, “Dynamics of real projective transformations”, Appl. Gen. Topol., vol. 19, no. 2, pp. 239–244, Oct. 2018.

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Articles