Ergodic dynamical systems over the cartesian power of the ring of p-adic integers
Tóm tắt
For any 1-lipschitz ergodic map F: ℤ
↦ ℤ
, k >1 ∈ ℕ, there are 1-lipschitz ergodic map G: ℤ
p
↦ ℤ
p
and two bijections H
k
, T
k, P
that
$G = H_k \circ T_{k,P} \circ F \circ H_k^{ - 1} andF = H_k^{ - 1} \circ T_{k,P - 1} \circ G \circ H_k $
.
Tài liệu tham khảo
V. Anashin and A. Khrennikov, Applied Algebraic Dynamics (de Gruyter Expos. Math., Berlin, 2009).
B. Dragovich, A. Yu. Khrennikov, S. V. Kozyrev and I. V. Volovich, “On p-adic mathematical physics,” p-Adic Numbers Ultr. Anal. Appl. 1(1), 1–17 (2009).
V. Anashin, “Uniformly distributed sequences over p-adic integers,” Number Theoretic and Algebraic Methods in Computer Science, pp. 1–18 (World Sci. Publ., Singapore, 1998).
V. Anashin, “Uniformly distributed sequences in computer algebra or how to construct program generators of random numbers,” J. Math. Sciences 89(4), 1355–1390 (1998).
V. Anashin, “Uniformly distributed sequences of p-adic integers,” Discr. Math. Appl. 12(6), 527–590 (2002).
V. Anashin, A. Khrennikov and E. Yurova, “T-Funtions revisited: New criteria for bijectivity/transitivity,” Designs Codes Crypt. 71(3), 383–407 (2014).