论文信息 - Composition of Involutive Power Series, and Reversible Series

Composition of Involutive Power Series, and Reversible Series

For each natural number n, we characterise the invertible series (under composition) that are the composition of n proper involutions. We work with formal power series in one variable over a field of characteristic zero. We also describe the reversible series (those conjugate to their own inverses), and the series that are the composition of n reversible series.

A. O’Farrell | Anthony G. O’Farrell

[1] N. Fine,et al. On the Group of Homeomorphisms of an Arc , 1955 .

[2] H. Cartan. Elementary Theory of Analytic Functions of One or Several Complex Variables , 1963 .

[3] A Complete Classification for Pairs of Real Analytic Curves in the Complex Plane with Tangential Intersection , 2005 .

[4] B. Malgrange. Travaux d'Ecalle et de Martinet-Ramis sur les systèmes dynamiques , 1982 .

[5] Jonathan D. Lubin. Nonarchimedean dynamical systems , 1994 .

[6] Normal forms of local diffeomorphisms on the real line , 1968 .

[7] L. Liverpool. Fractional Iteration Near a Fix Point of Multiplier 1 , 1975 .

[8] Dan Segal,et al. New Horizons in pro-p Groups , 2000 .

[9] R. Camina. The Nottingham Group , 2000 .

[10] I. N. Baker. Permutable power series and regular iteration , 1962, Journal of the Australian Mathematical Society.

[11] W. Jarczyk. Reversibility of interval homeomorphisms without fixed points , 2002 .