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Articles

Chaotic behaviour of countable products of homeomorphism groups

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Pages 1287-1312 | Received 13 Apr 2022, Accepted 11 Jun 2022, Published online: 01 Jul 2022

References

  • E. Akin, J. Auslander, and K. Berg, When is a transitive map chaotic?, in Convergence in Ergodic Theory and Probability, V. Bergelson, P. March and J. Rosenblatt, eds., Gruyter, Berlin, 1996, pp. 25–40.
  • S. Albeverio, A.Y. Khrennikov, and V.M. Shelkovich, Theory of p-Adic Distributions: Linear and Nonlinear Models, Cambridge University Press, New York, 2010.
  • D. Assaf and S. Gadbois, Definition of chaos, Am. Math. Mon. 99(9) (1992), pp. 865–865.
  • J. Banks, J. Brooks, G. Cairns, G. Davis, and P. Stacey, On Devaney's definition of chaos, Am. Math. Mon. 99(4) (1992), pp. 332–334.
  • A. Barzanouni, M.S. Divandar, and E. Shah, On properties of expansive group actions, Acta Math. Vietnam. 44(4) (2019), pp. 923–934.
  • Y.V. Bazaikin, A.S. Galaev, and N.I. Zhukova, Chaos in Cartan foliations, Chaos Interdiscip. J. Nonlinear Sci. 30 (2020), Article ID 103116.
  • E.V. Bogolepova and N.I. Zhukova, Anosov actions of isometry groups on Lorentzian2-orbifolds, Lobachevskii Math. J. 42(14) (2021), pp. 3324–3335.
  • G. Cairns, G. Davis, D. Elton, A. Kolganova, and P. Perversi, Chaotic group actions, Enseign. Math.41 (1995), pp. 123–133.
  • G. Cairns and A. Kolganova, Chaotic actions of free groups, Nonlinearity 9(4) (1996), pp. 1015–1021.
  • G. Cairns, A. Kolganova, and A. Nielsen, Topological transitivity and mixing notions for group actions, Rocky Mt. J. Math. 37(2) (2007), pp. 371–397.
  • F. Chovanec, Cantor sets, Sci. Mil. J. 5(1) (2010), pp. 5–10.
  • R.L. Devaney, Linked twist mappings are almost Anosov, in In: Nitecki, Z., Robinson, C. (eds) Global Theory of Dynamical Systems. Lecture Notes in Mathematics, 819, Nitecki Z. and Robinson C, ed., Springer, Berlin, Heidelberg, 1980. pp. 121–145.
  • R.L. Devaney, An Introduction to Chaotic Dynamical Systems, Addisson Wesley, Redwood City, CA, 1986.
  • M.M. Deza and E. Deza, Encyclopedia of Distances, Springer, Berlin, Heidelberg, 2009.
  • R. Engelking, General Topology, Mir, Moscow, 1986.
  • M. Hirasawa and E. Kin, Determination of generalized horseshoe maps inducing all link types, Topol. Appl. 139(1–3) (2004), pp. 261–277.
  • A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, New York, 1997.
  • A. Kechris, Classical Descriptive Set Theory, Springer-Verlag, New York, 1995.
  • A.C. Naolekar and P. Sankaran, Chaotic group actions on manifolds, Topol. Appl. 107 (2000), pp. 233–243.
  • F. Polo, Sensitive dependence on initial conditions and chaotic group actions, Proc. Am. Math. Soc.138(8) (2010), pp. 2815–2826.
  • E.A. Rogozhina and N.I. Zhukova, Classification of compact Lorentzian 2-orbifolds with noncompact full isometry groups, Sib. Math. J. 53(6) (2012), pp. 1037–1050.
  • R. Sturman, J.M. Ottino, and S. Wiggins, The Mathematical Foundations of Mixing: The Linked Twist Map as a Paradigm in Applications: Micro to Macro, Fluids to Solids, Cambridge University Press, New York, 2006.
  • P. Scott, The geometries of 3-manifolds, Bull. Lond. Math. Soc. 15 (1983), pp. 401–487.
  • N.I. Zhukova, Minimal sets of Cartan foliations, Proc. Steklov Inst. Math. 256 (2007), pp. 105–135.

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