Dynamics of real projective transformations

Sharan Gopal

India

Birla Institute of Technology and Science - Pilani

Assistant Professor

Department of Mathematics

Srikanth Ravulapalli

India

University of Hyderabad

Research Scholar

School of Mathematics and Statistics

Submitted: 2017-08-26

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Accepted: 2018-02-05

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Published: 2018-10-04

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

topological entropy, zeta function, projective transformation

Supporting agencies:

ResearchInitiation Grant provided by BITS-Pilani

UGC - Senior ResearchFellow.

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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References:

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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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