Li-Yorke Chaotic Eigen Set of Direct Sum of Linear Operators-Reference-Cited by-同舟云学术

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Li-Yorke Chaotic Eigen Set of Direct Sum of Linear Operators

Published:2022-09-13 Issue: Volume:2 Page:165-168
ISSN:2732-9941
Container-title:PROOF
language:en
Short-container-title:

Author:

B., Sanooj¹,P. B. Vinodkumar²

Affiliation:

1. Department of Mathematics, College of Engineering Trivandrum, Thiruvananthapuram APJ Abdul Kalam Technological University, INDIA

2. Department of Mathematics, Rajagiri School of Engineering and Technology, Kochi APJ Abdul Kalam Technological University, INDIA

Abstract

The Li-Yorke chaotic eigen set of an operator consisting of all λ’s such that T- λI is Li-Yorke chaotic. In this paper, the Li-Yorke chaotic eigen set of the direct sum of linear operators is found to be the union of Li- Yorke chaotic sets of the corresponding operators. Also we discuss about the Li-Yorke chaotic eigen set of compact operators, normal operators and self adjoint operators.

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

Reference19 articles.

1. F. Bayart, E. Matheron, Dynamics of Linear Operators (1st ed.) (2009), Cambridge Tracts in Mathematics, 175, Cambridge University Press, Cambridge.

2. K. G. Grosse Erdmann, A. P. Manguillot, Linear Chaos (2011), Springer Universitext.

3. T. Li, J. A. Yorke, Period three implies chaos, Amer. Math. Monthly. (1975), 82, 985-992

4. B. Sanooj, P. B. Vinodkumar, Li-Yorke chaotic eigen set of the backward shift operator on ` 2 (N), Concr. Oper. (2020), 7, 180-182

5. T. Bermudez, A. Bonilla, F. Martnez Gimenez, A. Peris, Li-Yorke and distributionally chaotic operators, J. Math. Anal. Appl. (2011), 373, 83- 93

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