Dynamics of real projective transformations

Sharan Gopal, Srikanth Ravulapalli
DOI: https://doi.org/10.4995/agt.2018.7962

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.

Keywords

topological entropy; zeta function; projective transformation

Subject classification

54H20; 37B40.

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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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Universitat Politècnica de València

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