Applied General Topology

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Applied General Topology publica artículos de investigación originales relacionados con las interacciones entre la topología general y otras disciplinas matemáticas así como los resultados topológicos con aplicaciones a otras áreas de la ciencia, y el desarrollo de teorías topológicas de importancia para permitir futuras aplicaciones.

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Browsing Applied General Topology by Sponsor "Department of Science and Technology, Ministry of Science and Technology, India"

Now showing 1 - 5 of 5
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    A note on measure and expansiveness on uniform spaces
    (Universitat Politècnica de València, 2019-04-01) Das, Pramod; Das, Tarun; Department of Science and Technology, Ministry of Science and Technology, India
    [EN] We prove that the set of points doubly asymptotic to a point has measure zero with respect to any expansive outer regular measure for a bi-measurable map on a separable uniform space. Consequently, we give a class of measures which cannot be expansive for Denjoy home-omorphisms on S1. We then investigate the existence of expansive measures for maps with various dynamical notions. We further show that measure expansive (strong measure expansive) homeomorphisms with shadowing have periodic (strong periodic) shadowing. We relate local weak specification and periodic shadowing for strong measure expansive systems.
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    Existence of Picard operator and iterated function system
    (Universitat Politècnica de València, 2020-04-03) Garg, Medha; Chandok, Sumit; Department of Science and Technology, Ministry of Science and Technology, India
    [EN] In this paper, we define weak θm− contraction mappings and give a new class of Picard operators for such class of mappings on a complete metric space. Also, we obtain some new results on the existence and uniqueness of attractor for a weak θm− iterated multifunction system. Moreover, we introduce (α, β, θm)− contractions using cyclic (α, β)− admissible mappings and obtain some results for such class of mappings without the continuity of the operator. We also provide an illustrative example to support the concepts and results proved herein.
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    Periodic points of solenoidal automorphisms in terms of inverse limits
    (Universitat Politècnica de València, 2021-10-01) Gopal, Sharan; Imam, Faiz; Department of Science and Technology, Ministry of Science and Technology, India
    [EN] In this paper, we describe the periodic points of automorphisms of a one dimensional solenoid, considering it as the inverse limit, lim←k (S 1 , γk) of a sequence (γk) of maps on the circle S 1 . The periodic points are discussed for a class of automorphisms on some higher dimensional solenoids also.
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    The class of simple dynamics systems
    (Universitat Politècnica de València, 2020-10-01) Ali Akbar, Kamaludheen; Department of Science and Technology, Ministry of Science and Technology, India
    [EN] In this paper, we study the class of simple dynamical systems on R induced by continuous maps having finitely many non-ordinary points. We characterize this class using labeled digraphs and dynamically independent sets. In fact, we classify dynamical systems up to their number of non-ordinary points. In particular, we discuss about the class of continuous maps having unique non-ordinary point, and the class of continuous maps having exactly two non-ordinary points.
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    Topological dynamics on hyperspaces
    (Universitat Politècnica de València, 2010-04-01) Sharma, Puneet; Nagar, Anima; Department of Science and Technology, Ministry of Science and Technology, India; Council of Scientific and Industrial Research, India
    [EN] In this paper we wish to relate the dynamics of the base map to the dynamics of the induced map. In the process, we obtain conditions on the endowed hyperspace topology under which the chaotic behaviour of the map on the base space is inherited by the induced map on the hyperspace. Several of the known results come up as corollaries to our results. We also discuss some metric related dynamical properties on the hyperspace that cannot be deduced for the base dynamics.