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Dynamics of the $p$adic shift and applications
1.  400 E 71 St. Apt. 5B, New York, NY 10021, United States 
2.  Massachusetts Institute of Technology, Cambridge, MA 02139, United States, United States 
3.  Williams College, Williamstown, MA 01267, United States 
References:
[1] 
V. Anashin and A. Khrennikov, "Applied Algebraic Dynamics," volume 49 of de Gruyter Expositions in Mathematics, Walter de Gruyter & Co., Berlin, 2009. 
[2] 
D. K. Arrowsmith and F. Vivaldi, Some $p$adic representations of the Smale horseshoe, Phys. Lett. A, 176 (1993), 292294. doi: 10.1016/03759601(93)90920U. 
[3] 
J. Bryk and C. E. Silva, Measurable dynamics of simple $p$adic polynomials, Amer. Math. Monthly, 112 (2005), 212232. doi: 10.2307/30037439. 
[4] 
N. D. Elkies, Mahler's theorem on continuous $p$adic maps via generating functions,, , (). 
[5] 
F. Q. Gouvêa, "$p$adic Numbers, An Introduction," Universitext. SpringerVerlag, Berlin, 1993. 
[6] 
A. Yu. Khrennikov and M. Nilson, "$p$adic Deterministic and Random Dynamics," volume 574 of Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht, 2004. 
[7] 
J. Kingsbery, A. Levin, A. Preygel, and C. E. Silva, On measurepreserving $C^1$ transformations of compactopen subsets of nonArchimedean local fields, Trans. Amer. Math. Soc., 361 (2009), 6185. doi: 10.1090/S0002994708046862. 
[8] 
A. V. Mikhaĭlov, The central limit theorem for a $p$adic shift. I, in "Analytic Number Theory (Russian)," Petrozavodsk. Gos. Univ., Petrozavodsk, (1986), 6068, 92. 
[9] 
A. M. Robert, "A Course in $p$adic Analysis," volume 198 of Graduate Texts in Mathematics, SpringerVerlag, New York, 2000. 
[10] 
C. E. Silva, "Invitation to Ergodic Theory," volume 42 of Student Mathematical Library, American Mathematical Society, Providence, RI, 2008. 
[11] 
J. H. Silverman, "The Arithmetic of Dynamical Systems," volume 241 of Graduate Texts in Mathematics, Springer, New York, 2007. 
[12] 
D. Verstegen, $p$adic dynamical systems, in "Number Theory and Physics (Les Houches, 1989)," volume 47 of Springer Proc. Phys., Springer, Berlin, (1990), 235242. 
[13] 
C. F. Woodcock and N. P. Smart, $p$adic chaos and random number generation, Experiment. Math., 7 (1998), 333342. 
show all references
References:
[1] 
V. Anashin and A. Khrennikov, "Applied Algebraic Dynamics," volume 49 of de Gruyter Expositions in Mathematics, Walter de Gruyter & Co., Berlin, 2009. 
[2] 
D. K. Arrowsmith and F. Vivaldi, Some $p$adic representations of the Smale horseshoe, Phys. Lett. A, 176 (1993), 292294. doi: 10.1016/03759601(93)90920U. 
[3] 
J. Bryk and C. E. Silva, Measurable dynamics of simple $p$adic polynomials, Amer. Math. Monthly, 112 (2005), 212232. doi: 10.2307/30037439. 
[4] 
N. D. Elkies, Mahler's theorem on continuous $p$adic maps via generating functions,, , (). 
[5] 
F. Q. Gouvêa, "$p$adic Numbers, An Introduction," Universitext. SpringerVerlag, Berlin, 1993. 
[6] 
A. Yu. Khrennikov and M. Nilson, "$p$adic Deterministic and Random Dynamics," volume 574 of Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht, 2004. 
[7] 
J. Kingsbery, A. Levin, A. Preygel, and C. E. Silva, On measurepreserving $C^1$ transformations of compactopen subsets of nonArchimedean local fields, Trans. Amer. Math. Soc., 361 (2009), 6185. doi: 10.1090/S0002994708046862. 
[8] 
A. V. Mikhaĭlov, The central limit theorem for a $p$adic shift. I, in "Analytic Number Theory (Russian)," Petrozavodsk. Gos. Univ., Petrozavodsk, (1986), 6068, 92. 
[9] 
A. M. Robert, "A Course in $p$adic Analysis," volume 198 of Graduate Texts in Mathematics, SpringerVerlag, New York, 2000. 
[10] 
C. E. Silva, "Invitation to Ergodic Theory," volume 42 of Student Mathematical Library, American Mathematical Society, Providence, RI, 2008. 
[11] 
J. H. Silverman, "The Arithmetic of Dynamical Systems," volume 241 of Graduate Texts in Mathematics, Springer, New York, 2007. 
[12] 
D. Verstegen, $p$adic dynamical systems, in "Number Theory and Physics (Les Houches, 1989)," volume 47 of Springer Proc. Phys., Springer, Berlin, (1990), 235242. 
[13] 
C. F. Woodcock and N. P. Smart, $p$adic chaos and random number generation, Experiment. Math., 7 (1998), 333342. 
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