Groups Having Elements Conjugate to Their Squares and Connections with Dynamical Systems

References

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[2]
G. R. Goodson, “Ergodic Dynamical Systems Conjugate to Their Composition Squares,” Journal of Acta Mathematica Universitatis Comenianae, Vol. 71, No. 7, 2002, pp. 201-210.

[3]
G. R. Goodson, “Spectral Properties of Ergodic Dyna- mical Systems Conjugate to Their Composition Squares,” Colloquium Mathematicum, Vol. 107, 2007, pp. 99-118.

[4]
B. Hasselblatt and A. Katok, “A First Course in Dynamical Systems,” Cambridge University Press, Cambridge, 2003.

[5]
P. Walters, “An Introduction to Ergodic Theory,” Springer Verlag, Berlin, 1982.

[6]
A. I. Danilenko, “Weakly Mixing Rank-One Transformations Conjugate to Their Squares,” Studia Mathematica, Vol. 187, No. 1, 2008, pp. 75-93.

[7]
B. Marcus, “Unique Ergodicity of the Horocycle Flow: Variable Negative Curvature Case,” Israel Journal of Mathematics, Vol. 21, No. 2-3, 1975, pp. 133-144.

[8]
R. L. Devaney, “Chaotic Dynamical Systems,” Benja- min Cummings Publishing Company, California, 1986.

[9]
N. J. Fine and G. E. Schweigert, “On the Group of Homeomorphisms of an Arc,” Annals of Mathematics, Vol. 62, No. 2, 1955, pp. 237-253.

[10] M. Kuczma, “On the Functional Equation ,” Annales Polonici Mathematici, Vol. 11, 1961, pp. 161-175.

[11]
J. L. King. “The Commutant is the Weak Closure of the Powers, for Rank-One Transformations,” Ergodic Theory and Dynamical Systems, Vol. 6, No. 3, 1983, pp. 363-384.

[12]
P. R. Halmos, “Ergodic Theory,” Chelsea Publishing Company, Vermont, 1956.

[13]
E. Hewitt and K. A. Ross, “Abstract Harmonic Analysis,” 2nd Edition, Springer-Verlag, Berlin, 1979.

[14]
N. Gill, A. G. O’Farell and I. Short. “Reversibility in the Group of Homeomorphisms of the Circle,” Bulletin of the London Mathematical Society, Vol. 41, No. 5, 2009, pp. 885-897.