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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), 292-294.
doi: 10.1016/0375-9601(93)90920-U. |
[3] |
J. Bryk and C. E. Silva, Measurable dynamics of simple $p$-adic polynomials, Amer. Math. Monthly, 112 (2005), 212-232.
doi: 10.2307/30037439. |
[4] |
N. D. Elkies, Mahler's theorem on continuous $p$-adic maps via generating functions, http://www.math.harvard.edu/ elkies/Misc/mahler.pdf. |
[5] |
F. Q. Gouvêa, "$p$-adic Numbers, An Introduction," Universitext. Springer-Verlag, 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 measure-preserving $C^1$ transformations of compact-open subsets of non-Archimedean local fields, Trans. Amer. Math. Soc., 361 (2009), 61-85.
doi: 10.1090/S0002-9947-08-04686-2. |
[8] |
A. V. Mikhaĭlov, The central limit theorem for a $p$-adic shift. I, in "Analytic Number Theory (Russian)," Petrozavodsk. Gos. Univ., Petrozavodsk, (1986), 60-68, 92. |
[9] |
A. M. Robert, "A Course in $p$-adic Analysis," volume 198 of Graduate Texts in Mathematics, Springer-Verlag, 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), 235-242. |
[13] |
C. F. Woodcock and N. P. Smart, $p$-adic chaos and random number generation, Experiment. Math., 7 (1998), 333-342. |
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), 292-294.
doi: 10.1016/0375-9601(93)90920-U. |
[3] |
J. Bryk and C. E. Silva, Measurable dynamics of simple $p$-adic polynomials, Amer. Math. Monthly, 112 (2005), 212-232.
doi: 10.2307/30037439. |
[4] |
N. D. Elkies, Mahler's theorem on continuous $p$-adic maps via generating functions, http://www.math.harvard.edu/ elkies/Misc/mahler.pdf. |
[5] |
F. Q. Gouvêa, "$p$-adic Numbers, An Introduction," Universitext. Springer-Verlag, 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 measure-preserving $C^1$ transformations of compact-open subsets of non-Archimedean local fields, Trans. Amer. Math. Soc., 361 (2009), 61-85.
doi: 10.1090/S0002-9947-08-04686-2. |
[8] |
A. V. Mikhaĭlov, The central limit theorem for a $p$-adic shift. I, in "Analytic Number Theory (Russian)," Petrozavodsk. Gos. Univ., Petrozavodsk, (1986), 60-68, 92. |
[9] |
A. M. Robert, "A Course in $p$-adic Analysis," volume 198 of Graduate Texts in Mathematics, Springer-Verlag, 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), 235-242. |
[13] |
C. F. Woodcock and N. P. Smart, $p$-adic chaos and random number generation, Experiment. Math., 7 (1998), 333-342. |
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