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Various Types of Shadowing and Specification on Uniform Spaces

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Abstract

We define topological pseudo orbital specification, topological weak specification, topological ergodic shadowing, topological \(\underline {d}\)-shadowing for a continuous map on a uniform space and show that they are equivalent for a uniformly continuous map with topological shadowing on a totally bounded uniform space.

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Acknowledgments

Authors are thankful to the referee for his/her valuable comments which has improved the paper significantly. The first author is supported by Department of Science and Technology, Government of India, under INSPIRE Fellowship (Resgistration No- IF150210) Program since March 2015.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, New Delhi, 110007, India

    Pramod Das & Tarun Das

Authors
  1. Pramod Das
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  2. Tarun Das
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Correspondence to Tarun Das.

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Das, P., Das, T. Various Types of Shadowing and Specification on Uniform Spaces. J Dyn Control Syst 24, 253–267 (2018). https://doi.org/10.1007/s10883-017-9388-1

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  • DOI: https://doi.org/10.1007/s10883-017-9388-1

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