About the Algebraic Yuzvinski Formula
Anna Giordano Bruno; Simone Virili
Topological Algebra and its Applications (2015)
- Volume: 3, Issue: 1, page 114-147
- ISSN: 2299-3231
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top- [1] R. L. Adler, A. G. Konheim and M. H. McAndrew, Topological entropy, Trans. Amer. Math. Soc. 114 (1965), 309–319. Zbl0127.13102
- [2] R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971), 401–414. Zbl0212.29201
- [3] D. Dikranjan and A. Giordano Bruno, Entropy on Abelian groups, submitted ; arXiv:1007.0533. Zbl06591707
- [4] D. Dikranjan and A. Giordano Bruno, The Bridge Theorem for totally disconnected LCA groups, Topology Appl. 169 (2014) no. 1, 21–32. [WoS] Zbl1322.37007
- [5] D. Dikranjan and A. Giordano Bruno, Limit free computation of entropy, Rend. Istit.Mat. Univ. Trieste 44 (2012), 297–312. Zbl1277.37031
- [6] D. Dikranjan and A. Giordano Bruno, Topological entropy and algebraic entropy for group endomorphisms, Proceedings ICTA2011 Islamabad, Pakistan July 4-10 2011 Cambridge Scientific Publishers, 133–214. Zbl1300.54002
- [7] D. Dikranjan and A. Giordano Bruno, The connection between topological and algebraic entropy, Topology Appl. 159 (2012) no.13, 2980–2989. [WoS] Zbl1256.54061
- [8] D. Dikranjan and A. Giordano Bruno, The Pinsker subgroup of an algebraic flow, J. Pure Appl. Algebra 216 (2012) no.2, 364–376. [WoS] Zbl1247.37014
- [9] D. Dikranjan, A. Giordano Bruno, L. Salce and S.Virili, Intrinsic algebraic entropy, J. Pure Appl. Algebra 219 (2015) 2933– 2961. [WoS] Zbl06409606
- [10] D. Dikranjan, B. Goldsmith, L. Salce and P. Zanardo, Algebraic entropy for Abelian groups, Trans. Amer. Math. Soc. 361 (2009), 3401–3434. Zbl1176.20057
- [11] D. Dikranjan, K. Gong and P. Zanardo, Endomorphisms of Abelian groups with small algebraic entropy, Linear Algebra Appl. 439 (2013) no.7, 1894–1904. [WoS] Zbl1320.37013
- [12] D. Dikranjan, M. Sanchis and S. Virili, New and old facts about entropy on uniform spaces and topological groups, Topology Appl. 159 (2012) no.7, 1916–1942. [WoS] Zbl1242.54005
- [13] M. Einsiedler and T. Ward, Ergodic Theory (with a view towards Number Theory), Graduate Texts in Mathematics Volume 259, 2011. [WoS] Zbl1206.37001
- [14] G. Everest and T. Ward, Heights of Polynomials and Entropy in Algebraic Dynamics, Springer Verlag, 1999. Zbl0919.11064
- [15] A. Giordano Bruno and S. Virili, Algebraic Yuzvinski Formula, J. Algebra 423 (2015) 114–147. [WoS] Zbl06377569
- [16] E. Hewitt and K. A. Ross, Abstract harmonic analysis I, Springer-Verlag, Berlin-Heidelberg-New York, 1963. Zbl0115.10603
- [17] E. Hironaka, What is. . .Lehmer’s number?, Not. Amer. Math. Soc. 56 (2009) no. 3, 374–375. Zbl1163.11069
- [18] B. M. Hood, Topological entropy and uniform spaces, J. London Math. Soc. (2) 8 (1974), 633–641. [Crossref] Zbl0291.54051
- [19] I. Kaplansky, Infinite Abelian groups, University of Michigan Publications in Mathematics, no. 2, Ann Arbor, University of Michigan Press, 1954. Zbl0057.01901
- [20] N. Koblitz, p-adic Numbers, p-adic Analysis, and Zeta-Functions, Second Edition, Graduate Texts in Mathematics 58, Springer-Verlag New York, Berlin, Heidelberg, Tokyo, 1984. Zbl0364.12015
- [21] L. Kronecker, Zwei Sätze über Gleichungen mit ganzzahligen Coeflcienten, Jour. Reine Angew. Math. 53 (1857), 173–175.
- [22] D. H. Lehmer, Factorization of certain cyclotomic functions, Ann. of Math. (2) 34 (1933), 461-479. Zbl0007.19904
- [23] D. A. Lind and T. Ward, Automorphisms of solenoids and p-adic entropy, Ergod. Th. & Dynam. Sys. 8 (1988), 411–419. Zbl0634.22005
- [24] K. Mahler, On some inequalities for polynomials in several variables, J. London Math. Soc. 37 (1962), 341–344. Zbl0105.06301
- [25] M. J. Mossinghoff, Lehmer’s Problem web page, http://www.cecm.sfu.ca/ mjm/Lehmer/lc.html.
- [26] J. Peters, Entropy on discrete Abelian groups, Adv. Math. 33 (1979), 1–13. Zbl0421.28019
- [27] J. Peters, Entropy of automorphisms on L.C.A. groups, Pacific J. Math. 96 (1981) no.2, 475–488. Zbl0478.28010
- [28] F. Quadros Gouvêa, p-adic numbers: an introduction, Springer-Verlag, Berlin-Heidelberg-New York, 1997.
- [29] C. Smyth, TheMahler measure of algebraic numbers: a survey. Number theory and polynomials, 322–349, LondonMath. Soc. Lecture Note Ser., 352, Cambridge Univ. Press, Cambridge, 2008. Zbl1334.11081
- [30] L. N. Stojanov, Uniqueness of topological entropy for endomorphisms on compact groups, Boll. Un. Mat. Ital. B 7 (1987) no. 3, 829–847. Zbl0648.22002
- [31] S. Virili, Entropy for endomorphisms of LCA groups, Topology Appl. 159 (2012) no.9, 2546–2556. Zbl1243.22007
- [32] P. Walters, An Introduction to Ergodic Theory, Springer-Verlag, New-York, 1982. Zbl0475.28009
- [33] M. D. Weiss, Algebraic and other entropies of group endomorphisms, Math. Systems Theory 8 (1974/75) no.3, 243–248. Zbl0298.28014
- [34] A. Weil, Basic Number Theory, third edition, Springer Verlag, New York (1974).
- [35] S. A. Yuzvinski, Metric properties of endomorphisms of compact groups, Izv. Acad. Nauk SSSR, Ser.Mat. 29 (1965), 1295– 1328 (in Russian). English Translation: Amer. Math. Soc. Transl. (2) 66 (1968), 63–98.
- [36] S. A. Yuzvinski, Computing the entropy of a group endomorphism, Sibirsk.Mat. Z. 8 (1967), 230–239 (in Russian). English Translation: Siberian Math. J. 8 (1968), 172–178.
- [37] P. Zanardo, Yuzvinski’s Formula, unpublished notes.