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A Review on Furstenberg Family in Dynamical Systems

Affiliations

  • Department of Mathematics, JIL Information Technology, Sector-128, Noida, Uttar Pradesh, India
  • Amity Institute of Applied Science, Amity University, Sector-125, Noida, Uttar Pradesh, India
  • Department of Mathematics, Kuruskhetra University, Kurukshetra, Haryana, India

Abstract


Objective: The purpose of this paper to highlight the comprehensive overview of Furstenberg family which creates a bridge for future research. Methods: For this, a detailed study of topology as well as dynamical systems is required. In addition to this a deep study of the term chaos as well as Furstenberg family is required. Also, the main of application of dynamical system is chaos theories which play an important role in the study of Furstenberg Family using topology. Findings: This paper demonstrates the development of dynamical system and some important terms related to dynamical systems such as topological entropy, weakly mixing sets, topologically transitive, period, orbit etc are well explained. The beauty of this study lies in its overview on the term chaos as well as its role in the study of dynamical system using topology. This paper brings a great attention on the term Furstenberg Family which is studied on the platform made by the combination of dynamical system and topology. Application: This paper gives a fruitful overview on Furstenberg family in topological dynamical systems having chaotic nature.

Keywords

Chaos Mathematics Subject Classification: 37D45, 37N05, 37C25, 54H20, Dynamical Systems, Furstenberg Family, Sensitivity, Transitivity.

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