# American Institute of Mathematical Sciences

June  2009, 2(2): 269-285. doi: 10.3934/dcdss.2009.2.269

 1 Mathematics Department, The Ohio State University, 231 W 18th Avenue, Columbus, OH 43210, United States

Received  February 2008 Revised  December 2008 Published  April 2009

We introduce a family of adic transformations on diagrams that are nonstationary and nonsimple. This family includes some previously studied adic transformations such as the Pascal and Euler adic transformations. We give examples of particular adic transformations with roots of unity and we show as well that the Euler adic is totally ergodic. We show that the Euler adic and a disjoint subfamily of adic transformations are loosely Bernoulli.
Citation: Sarah Bailey Frick. Limited scope adic transformations. Discrete and Continuous Dynamical Systems - S, 2009, 2 (2) : 269-285. doi: 10.3934/dcdss.2009.2.269
 [1] Vladimir Anashin, Andrei Khrennikov, Ekaterina Yurova. Ergodicity criteria for non-expanding transformations of 2-adic spheres. Discrete and Continuous Dynamical Systems, 2014, 34 (2) : 367-377. doi: 10.3934/dcds.2014.34.367 [2] James Kingsbery, Alex Levin, Anatoly Preygel, Cesar E. Silva. Dynamics of the $p$-adic shift and applications. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 209-218. doi: 10.3934/dcds.2011.30.209 [3] Andrew Klapper. The asymptotic behavior of N-adic complexity. Advances in Mathematics of Communications, 2007, 1 (3) : 307-319. doi: 10.3934/amc.2007.1.307 [4] Frédéric Bernicot, Bertrand Maury, Delphine Salort. A 2-adic approach of the human respiratory tree. Networks and Heterogeneous Media, 2010, 5 (3) : 405-422. doi: 10.3934/nhm.2010.5.405 [5] Wacław Marzantowicz, Piotr Maciej Przygodzki. Finding periodic points of a map by use of a k-adic expansion. Discrete and Continuous Dynamical Systems, 1999, 5 (3) : 495-514. doi: 10.3934/dcds.1999.5.495 [6] Raf Cluckers, Julia Gordon, Immanuel Halupczok. Motivic functions, integrability, and applications to harmonic analysis on $p$-adic groups. Electronic Research Announcements, 2014, 21: 137-152. doi: 10.3934/era.2014.21.137 [7] Aihua Fan, Shilei Fan, Lingmin Liao, Yuefei Wang. Minimality of p-adic rational maps with good reduction. Discrete and Continuous Dynamical Systems, 2017, 37 (6) : 3161-3182. doi: 10.3934/dcds.2017135 [8] Farrukh Mukhamedov, Otabek Khakimov. Chaotic behavior of the P-adic Potts-Bethe mapping. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 231-245. doi: 10.3934/dcds.2018011 [9] Saadoun Mahmoudi, Karim Samei. Codes over $\frak m$-adic completion rings. Advances in Mathematics of Communications, 2020  doi: 10.3934/amc.2020122 [10] Ilwoo Cho. Certain $*$-homomorphisms acting on unital $C^{*}$-probability spaces and semicircular elements induced by $p$-adic number fields over primes $p$. Electronic Research Archive, 2020, 28 (2) : 739-776. doi: 10.3934/era.2020038 [11] Denis Mercier. Spectrum analysis of a serially connected Euler-Bernoulli beams problem. Networks and Heterogeneous Media, 2009, 4 (4) : 709-730. doi: 10.3934/nhm.2009.4.709 [12] Jong Yeoul Park, Sun Hye Park. On uniform decay for the coupled Euler-Bernoulli viscoelastic system with boundary damping. Discrete and Continuous Dynamical Systems, 2005, 12 (3) : 425-436. doi: 10.3934/dcds.2005.12.425 [13] Ammar Khemmoudj, Imane Djaidja. General decay for a viscoelastic rotating Euler-Bernoulli beam. Communications on Pure and Applied Analysis, 2020, 19 (7) : 3531-3557. doi: 10.3934/cpaa.2020154 [14] Maja Miletić, Dominik Stürzer, Anton Arnold. An Euler-Bernoulli beam with nonlinear damping and a nonlinear spring at the tip. Discrete and Continuous Dynamical Systems - B, 2015, 20 (9) : 3029-3055. doi: 10.3934/dcdsb.2015.20.3029 [15] Fathi Hassine. Asymptotic behavior of the transmission Euler-Bernoulli plate and wave equation with a localized Kelvin-Voigt damping. Discrete and Continuous Dynamical Systems - B, 2016, 21 (6) : 1757-1774. doi: 10.3934/dcdsb.2016021 [16] Kaïs Ammari, Denis Mercier, Virginie Régnier, Julie Valein. Spectral analysis and stabilization of a chain of serially connected Euler-Bernoulli beams and strings. Communications on Pure and Applied Analysis, 2012, 11 (2) : 785-807. doi: 10.3934/cpaa.2012.11.785 [17] Louis Tebou. Well-posedness and stabilization of an Euler-Bernoulli equation with a localized nonlinear dissipation involving the $p$-Laplacian. Discrete and Continuous Dynamical Systems, 2012, 32 (6) : 2315-2337. doi: 10.3934/dcds.2012.32.2315 [18] Louis Tebou. Energy decay estimates for some weakly coupled Euler-Bernoulli and wave equations with indirect damping mechanisms. Mathematical Control and Related Fields, 2012, 2 (1) : 45-60. doi: 10.3934/mcrf.2012.2.45 [19] Gen Qi Xu, Siu Pang Yung. Stability and Riesz basis property of a star-shaped network of Euler-Bernoulli beams with joint damping. Networks and Heterogeneous Media, 2008, 3 (4) : 723-747. doi: 10.3934/nhm.2008.3.723 [20] Marcelo Moreira Cavalcanti. Existence and uniform decay for the Euler-Bernoulli viscoelastic equation with nonlocal boundary dissipation. Discrete and Continuous Dynamical Systems, 2002, 8 (3) : 675-695. doi: 10.3934/dcds.2002.8.675

2020 Impact Factor: 2.425