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Dynamical Systems
An International Journal
Volume 39, 2024 - Issue 1
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Research Article

Weaker forms of specification for maps on uniform spaces

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Pages 150-165 | Received 25 May 2022, Accepted 11 Jul 2023, Published online: 18 Jul 2023

References

  • N. Aoki, Topological Dynamics, Topics in General Topology Vol. 41, North-Holland Publishing Co., Amsterdam, 1989, pp. 625–740.
  • T. Arai, Devaney's and Li–Yorke's chaos in uniform spaces, J. Dyn. Control Syst. 24 (2018), pp. 93–100.
  • R. Bowen, Periodic points and measures for Axiom A diffeomorphisms, Trans. Am. Math. Soc. 154 (1971), pp. 377–397.
  • R. Bowen, Periodic orbits for hyperbolic flows, Am. J. Math. 94 (1972), pp. 1–30.
  • P. Das and T. Das, Various types of shadowing and specification on uniform spaces, J. Dyn. Control Syst. 24 (2018), pp. 253–267.
  • P. Das, A.G. Khan, and T. Das, Measure expansivity and specification for pointwise dynamics, Bull. Braz. Math. Soc. New Ser. 50 (2019), pp. 933–948.
  • R.L. Devaney, An Introduction to Chaotic Dynamical Systems, 2nd ed., Addison-Wesley, California, CA, 1989.
  • A. Fedeli and A.L. Donne, A note on the uniform limit of transitive dynamical systems, Bull. Belg. Math. Soc. Simon Stevin 16(1) (2009), pp. 59–66.
  • B.M. Hood, Topological entropy and uniform spaces, J. Lond. Math. Soc. s2-8 (1974), pp. 633–641.
  • J. Kelley, General Topology, D Van Nostrand Company, New York, NY, 1955.
  • A.G. Khan, P.K. Das, and T. Das, Pointwise dynamics under orbital convergence, Bull. Braz. Math. Soc. New Ser. 51 (2020), pp. 1001–1016.
  • C.A. Morales, Shadowable points, Dyn. Syst. 31 (2016), pp. 347–356.
  • W.L. Reddy, Pointwise expansion homeomorphisms, J. Lond. Math. Soc. s2-2 (1970), pp. 232–236.
  • S. Shah, R. Das, and T. Das, A note on uniform entropy for maps having topological specification property, Appl. Gen. Topol. 17 (2016), pp. 123–127.
  • S. Shah, R. Das, and T. Das, Specification property for topological spaces, J. Dyn. Control Syst. 22 (2016), pp. 615–622.
  • S. Shah, T. Das, and R. Das, Distributional Chaos on uniform spaces, Qual. Theory Dyn. Syst. 19(1) (2020), Article ID 4.
  • K. Sigmund, On dynamical systems with the specification property, Trans. Am. Math. Soc. 190 (1974), pp. 285–299.
  • A. Sklar and J. Smítal, Distributional chaos on compact metric spaces via specification properties, J. Math. Anal. Appl. 241 (2000), pp. 181–188.
  • J. Taylor, Chaos in topological spaces, Far East J. Dyn. Syst. 4 (2002), pp. 115–124.
  • N. Yadav and S. Shah, Li–Yorke chaos and topological distributional chaos in a sequence, Turk. J. Math. 46(4) (2022), pp. 1360–1368.
  • N. Yadav and S. Shah, Topological weak specification and distributional chaos on noncompact spaces, Int. J. Bifurc. Chaos Appl. Sci. Eng. 32(4) (2022), Article ID 2250048.
  • Q. Yan, J. Yin, and T. Wang, Some weak specification properties and strongly mixing, Chin. Ann. Math. Ser. B 38 (2017), pp. 1111–1118.
  • X. Ye and G. Zhang, Entropy points and applications, Trans. Am. Math. Soc. 359 (2007), pp. 6167–6186.

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