Dense uniform Li-Yorke chaos for linear operators on a Banach space

Abstract

This paper focuses on the dense uniform Li-Yorke chaos for linear operators on a Banach space. Some sufficient conditions and equivalent conditions are established under which the dynamical system is densely uniformly Li-Yorke chaotic. It is shown that there are plenty of densely uniformly Li-Yorke chaotic operators. For unilateral backward weighted shifts and bilateral backward weighted shifts on ${\ell }^p$, it is shown that Li-Yorke chaos is equivalent to dense uniform Li-Yorke chaos.

16 pages, Accepted by International Journal of Bifurcation and Chaos

References in corpus (3)

• Recent development of chaos theory in topological dynamics
• Chaos and Entropy for Interval Maps
• Chaos for endomorphisms of completely metrizable groups and linear operators on Fréchet spaces

Cited by in corpus (1)

• Chaotic discretization theorems for forced linear and nonlinear coupled oscillators