Measure-preservation criteria for 1-Lipschitz functions on Fq[[T]] in terms of the three bases of Carlitz polynomials, digit derivatives, and digit shifts

Abstract As a follow-up to our previous work [10] , we characterize the measure-preservation of 1-Lipschitz functions on F q [ [ T ] ] in terms of the three well-known bases: Carlitz polynomials, digit derivatives, and digit shifts.

[1]  Sangtae Jeong.  Characterization of ergodicity of T-adic maps on F2〚T〛 using digit derivatives basis , 2013 .

[2]  Ekaterina Yurova.  Van der Put basis and p-adic dynamics , 2010 .

[3]  Andrei Khrennikov,et al.  T-functions revisited: new criteria for bijectivity/transitivity , 2014, Des. Codes Cryptogr..

[4]  Sangtae Jeong.  A Comparison of the Carlitz and Digit Derivatives Bases in Function Field Arithmetic , 2000 .

[5]  M. Van Der Put.  Algébres de Fonctions Continues p-Adiques. II , 1968 .

[6]  V. S. Anachin.  Uniformly distributed sequences ofp-adic integers , 1994 .

[7]  Keith Conrad,et al.  The Digit Principle , 2000 .

[8]  Andrei Khrennikov,et al.  Applied Algebraic Dynamics , 2009 .

[9]  Sangtae Jeong.  Digit derivatives and application to zeta measures , 2004 .

[10]  Leonard Carlitz,et al.  A set of polynomials , 1940 .

[11]  Sangtae Jeong,et al.  Hyperdifferential Operators and Continuous Functions on Function Fields , 2001 .

[12]  K. Mahler.  p-adic numbers and their functions , 1981 .

[13]  Chunlan Li,et al.  Criteria of measure-preservation for 1-Lipschitz functions on Fq[[T]] in terms of the van der Put basis and its applications , 2016, Finite Fields Their Appl..

[14]  Fabien Durand,et al.  Minimal polynomial dynamics on the set of 3‐adic integers , 2009, 1208.2016.

[15]  Brian Alan Snyder.  Hyperdifferential operators on function fields and their applications , 2000 .

[16]  Carl G. Wagner,et al.  Interpolation series for continuous functions on π-adic completions of GF(q, x) , 1971 .

[17]  Sangtae Jeong,et al.  Measure-preservation criteria for a certain class of 1-lipschitz functions on Z p in mahler's expansion , 2017 .

[18]  Zifeng Yang.  Cn-Functions over completions of Fr[T] at finite places of Fr(T) , 2004 .

[19]  Ekaterina Yurova,et al.  Criteria of measure-preserving for p-adic dynamical systems in terms of the van der Put basis , 2012 .

[20]  Sangtae Jeong,et al.  Toward the ergodicity of p-adic 1-Lipschitz functions represented by the van der Put series☆ , 2012, 1210.5001.

[21]  Dongdai Lin,et al.  Ergodic theory over F2[[T]] , 2012, Finite Fields Their Appl..

[22]  Ekaterina Yurova.  On measure-preserving functions over ℤ3 , 2012 .

[23]  J. Silverman.  The Arithmetic of Dynamical Systems , 2007 .

[24]  Sangtae Jeong.  Shift operators and two applications to Fq[[T]] , 2014 .

[25]  Vladimir Anashin,et al.  Characterization of ergodicity of p-adic dynamical systems by using the van der Put basis , 2011 .

[26]  David Goss.  Fourier series, measures and divided power series in the theory of function fields , 1989 .