Publications

    Monographs

  1. L. Aussenhofer, D. Dikranjan, A. Giordano Bruno: Topological Groups and the Pontryagin-van Kampen Duality. An Introduction. De Gruyter Stud. Math., 83. De Gruyter, Berlin, 2022, xiv+376 pp. ISBN: 978-3-11-065349-6; 978-3-11-065355-7.

    2. Papers

  2. D. Dikranjan, R. Di Santo, A. Giordano Bruno, H. Weber: On the size of I-characterized subgroups of T. Preprint.
  3. D. Dikranjan, R. Di Santo, A. Giordano Bruno, H. Weber: Nested ideals and topologically u_I-torsion elements of the circle group. Submitted.
  4. D. Castelnovo, D. Dikranjan, A. Giordano Bruno, D. Spirito, S. Virili: A length function of Z[X_1,...,X_m]-modules and Mahler measure. To appear in the volume The Ideal Theory and Arithmetic of Rings, Monoids, and Semigroups, AMS Contemporary Mathematics.
  5. D. Dikranjan, R. Di Santo, A. Giordano Bruno, H. Weber: Topologically I-torsion elements of the circle. Comm. Algebra (2026).
  6. D. Dikranjan, R. Di Santo, A. Giordano Bruno, H. Weber: An introduction to I-characterized subgroups of the circle. Topol. Appl. 371 (2025), Paper No. 109366, 44 pp.
  7. H. Akin, D. Dikranjan, A. Giordano Bruno, D. Toller: The algebraic entropy of one-dimensional finitary linear cellular automata. J. Group Theory 27 (2024), no.4, 813-856.
  8. D. Dikranjan, A. Giordano Bruno, S. Virili: Ore localization of amenable monoid actions and applications towards entropy - addition formulas and the bridge theorem. Illinois J. Math. 67 (2023), no. 4, 715-787.
  9. D. Dikranjan, A. Giordano Bruno, N. Zava: Epimorphisms and closure operators of categories of semilattices. Quaest. Math. 46 (S1) (2023), 191-221.
  10. I. Castellano, A. Giordano Bruno, N. Zava: Weakly weightable generalized quasi-metric spaces and semilattices. Theoret. Comput. Sci. 977 (2023), Paper No. 114129, 29 pp.
  11. A. Giordano Bruno: Growth of groups and group endomorphisms. Adv. Group Theory Appl. 15 (2023), 35-62.
  12. G. Barbieri, D. Dikranjan, A. Giordano Bruno, H. Weber: Factorizable subgroups of the circle group. Topology Appl. 323 (2023), Paper No. 108283, 10 pp.
  13. D. Dikranjan, A. Fornasiero, A. Giordano Bruno, F. Salizzoni: The addition theorem for locally monotileable monoid actions. J. Pure Appl. Algebra 227 (2023), no. 1, Paper No. 107113, 35 pp.
  14. D. Dikranjan, A. Giordano Bruno, H.-P. Künzi, D. Toller, N. Zava: Generalized quasi-metric semilattices. Topology Appl. 309 (2022), Paper No. 107916, 35 pp.
  15. I. Castellano, D. Dikranjan, D. Freni, A. Giordano Bruno, D. Toller: Intrinsic entropy for generalized quasimetric semilattices. J. Algebra Appl. 21 (2022), no. 10, Paper No. 2250244, 24 pp.
  16. A. Biś, D. Dikranjan, A. Giordano Bruno, L. Stoyanov: Metric vs topological receptive entropy for semigroup actions. Qual. Theory Dyn. Syst. 20 (2021), no. 2, Paper No. 50, 41 pp.
  17. D. Dikranjan, A. Giordano Bruno, F. G. Russo: Finiteness of topological entropy for locally compact abelian groups. Glasg. Math. J. 63 (2021), no. 1, 81-105.
  18. A. Biś, D. Dikranjan, A. Giordano Bruno, L. Stoyanov: Topological entropy, upper Carathéodory capacity and fractal dimensions of semigroup actions. Colloq. Math. 163 (2021), no. 1, 131-151.
  19. A. Biś, D. Dikranjan, A. Giordano Bruno, L. Stoyanov: Algebraic entropies of commuting endomorphisms of torsion abelian groups. Rend. Semin. Mat. Univ. Padova 144 (2020), 45-60.
  20. A. Giordano Bruno, F. Salizzoni: Additivity of the algebraic entropy for locally finite groups with permutable finite subgroups. J. Group Theory 23 (2020), no. 5, 831-846.
  21. D. Dikranjan, A. Fornasiero, A. Giordano Bruno: Algebraic entropy for amenable semigroup actions. J. Algebra 556 (2020), 467-546.
  22. A. Giordano Bruno: A Bridge Theorem for the entropy of semigroup actions. Topol. Algebra Appl. 8 (2020), no. 1, 46-57.
  23. A. Giordano Bruno, P. Spiga: Milnor-Wolf Theorem for the growth of group endomorphisms. J. Algebra 546 (2020), 85-118.
  24. D. Dikranjan, A. Giordano Bruno: Entropy on normed semigroups (Towards a unifying approach to entropy). Dissertationes Math. 542 (2019), 90 pp.
  25. A. Giordano Bruno, M. Shlossberg, D. Toller: Algebraic entropy on strongly compactly covered groups. Topology Appl. 263 (2019), 117-140.
  26. I. Castellano, A. Giordano Bruno: Topological entropy on locally linearly compact vector spaces. Topology Appl. 252 (2019), 112-144.
  27. R. Di Santo, D. Dikranjan, A. Giordano Bruno: Characterized subgroups of the circle group. Ric. Mat. 67 (2018), no. 2, 625-655.
  28. I. Castellano, A. Giordano Bruno: Algebraic entropy on locally linearly compact vector spaces, Springer, Cham, 2017, 103-127. ISBN: 978-3-319-65872-8; 978-3-319-65874-2
  29. G. Barbieri, D. Dikranjan, A. Giordano Bruno, H. Weber: Dirichlet sets vs characterized subgroups. Topology Appl. 231 (2017), 50-76.
  30. A. Giordano Bruno, P. Spiga: Some properties of the growth and of the algebraic entropy of group endomorphisms. J. Group Theory 20 (2017), no. 4, 763-774.
  31. A. Giordano Bruno, S. Virili: Topological entropy in totally disconnected locally compact groups. Ergodic Theory Dynam. Systems 37 (2017), no. 7, 2163-2186.
  32. G. Barbieri, A. Giordano Bruno, H. Weber: Inclusions of characterized subgroups of R, Topology Appl. 221 (2017), 534-555.
  33. D. Dikranjan, A. Giordano Bruno: Entropy on abelian groups. Adv. Math. 298 (2016), 612-653.
  34. A. Giordano Bruno, S. Virili: About the Algebraic Yuzvinski Formula. Topol. Algebra Appl. 3 (2015), no. 1, 86-103.
  35. D. Dikranjan, A. Giordano Bruno, D. Impieri: Characterized subgroups of topological abelian groups. Axioms 4 (2015), 459-491.
  36. D. Dikranjan, A. Giordano Bruno, L. Salce, S. Virili: Intrinsic algebraic entropy. J. Pure Appl. Algebra 219 (2015), no. 7, 2933-2961.
  37. A. Giordano Bruno: Topological entropy for automorphisms of totally disconnected locally compact groups. Topology Proc. 45 (2015), 175-187.
  38. D. Dikranjan, A. Giordano Bruno: A factorization theorem for topological abelian groups. Comm. Algebra 43 (2015), no. 1, 212-224.
  39. A. Giordano Bruno, S. Virili: Algebraic Yuzvinski Formula. J. Algebra 423 (2015), 114-147.
  40. F. Berlai, D. Dikranjan, A. Giordano Bruno: Two ways of measuring chaos in locally compact totally disconnected groups. RIMS Kôkyûroku 1932 (2015), 60-66.
  41. D. Dikranjan, A. Giordano Bruno: The Bridge Theorem for totally disconnected LCA groups. Topology Appl. 169 (2014), 21-32.
  42. D. Dikranjan, A. Giordano Bruno, L. Salce, S. Virili: Fully inert subgroups. J. Group Theory 16 (2013), no. 6, 915-939.
  43. D. Dikranjan, A. Giordano Bruno: Compact groups with a dense free abelian subgroup. Rend. Istit. Mat. Univ. Trieste 45 (2013), 137-150.
  44. F. Berlai, D. Dikranjan, A. Giordano Bruno: Scale function vs Topological entropy. Topology Appl. 160 (2013), no. 18, 2314-2334.
  45. D. Dikranjan, A. Giordano Bruno: Discrete dynamical systems in group theory, Note Mat. 33 (2013), no. 1, 1-48.
  46. D. Dikranjan, A. Giordano Bruno: Entropy in a category. Appl. Categ. Structures 21 (2013), no. 1, 67-101.
  47. D. Dikranjan, A. Giordano Bruno: Limit free computation of entropy. Rend. Istit. Mat. Univ. Trieste 44 (2012), 297-312.
  48. A. Giordano Bruno, S. Virili: String numbers of abelian groups. J. Algebra Appl. 11 (2012), no. 4, 1250161, 30 pp.
  49. D. Dikranjan, A. Giordano Bruno: Topological entropy and algebraic entropy for group endomorphisms, Proceedings ICTA2011 Islamabad, Pakistan July 4-10 2011 Cambridge Scientific Publishers 133-214.
  50. D. Dikranjan, A. Giordano Bruno: The connection between topological and algebraic entropy. Topology Appl. 159 (2012), no. 13, 2980-2989.
  51. A. Giordano Bruno: Adjoint entropy vs Topological entropy. Topology Appl. 159 (2012), no. 9, 2404-2419.
  52. A. Giordano Bruno, L. Salce: A soft introduction to algebraic entropy. Arab. J. Math. (Springer) 1 (2012), no. 1, 69-87.
  53. D. Dikranjan, A. Giordano Bruno: The Pinsker subgroup of an algebraic flow. J. Pure Appl. Algebra 216 (2012), no. 2, 364-376.
  54. D. Dikranjan, A. Giordano Bruno: Functorial topologies and finite-index subgroups of abelian groups. Topology Appl. 158 (2011), no. 17, 2391-2407.
  55. D. Dikranjan, A. Giordano Bruno, S. Virili: Strings of group endomorphisms. J. Algebra Appl. 9 (2010), no. 6, 933-958.
  56. D. Dikranjan, A. Giordano Bruno, L. Salce: Adjoint algebraic entropy. J. Algebra 324 (2010), no. 3, 442-463.
  57. A. Giordano Bruno: Algebraic entropy of shift endomorphisms on products. Comm. Algebra 38 (2010), no. 11, 4155-4174.
  58. M. Akhavin, F. Ayatollah Zadeh Shirazi, D. Dikranjan, A. Giordano Bruno, A. Hosseini: Algebraic entropy of shift endomorphisms on abelian groups. Quaest. Math. 32 (2009), no. 4, 529-550.
  59. D. Dikranjan, A. Giordano Bruno, D. Shakhmatov: Minimal pseudocompact group topologies on free abelian groups. Topology Appl. 156 (2009), no. 12, 2039-2053.
  60. D. Dikranjan, A. Giordano Bruno: Arnautov's problems on semitopological isomorphisms. Appl. Gen. Topol. 10 (2009), no. 1, 85-119.
  61. A. Giordano Bruno: Extremal α-pseudocompact abelian groups. Forum Math. 21 (2009), no. 4, 639-659.
  62. D. Dikranjan, A. Giordano Bruno: w-Divisible groups. Topology Appl. 155 (2008), no. 4, 252-272.
  63. D. Dikranjan, A. Giordano Bruno: Pseudocompact totally dense subgroups. Proc. Amer. Math. Soc. 136 (2008), no. 3, 1093-1103.
  64. A. Giordano Bruno: Semitopological homomorphisms. Rend. Semin. Mat. Univ. Padova 120 (2008), 79-126.
  65. A. Giordano Bruno: Dense minimal pseudocompact subgroups of compact abelian groups. Topology Appl. 155 (2008), no. 17-18, 1919-1928.
  66. D. Dikranjan, A. Giordano Bruno, C. Milan: Weakly metrizable pseudocompact groups. Appl. Gen. Topol. 7 (2006), no. 1, 1-39.

    67. Ph.D. Thesis

  67. A. Giordano Bruno: Cardinal invariants of topological groups and applications to κ-pseudocompact groups, Tesi di Dottorato, Università degli Studi di Udine, relatore: Prof. D. Dikranjan (2008), pp. i-xvi, 1-117. pdf