Nonuniform Polynomial Dichotomy With Lyapunov Type Norms

Abstract

The paper considers a general concept of polynomial dichotomy which includes as particular cases some well-known dichotomy concepts. The main objective is to obtain some characterizations of the nonuniform polynomial dichotomy behavior with respect to a family of norms compatible with the projection families

On some growth concepts for dichotomic behaviors of evolution operators

“…In what follows, we maintain all the notations and the concepts presented in our previous papers (see [3] and also [4][5][6][7][8][9][10]).…”

“…Among the most significant concepts in this field are the exponential dichotomy and the polynomial dichotomy. The importance of the role played by these notions in the theory of dynamical systems is illustrated by the appearance of numerous papers in this domain for the uniform case ([3,10,14,18,23,24,30]) as well as for the nonuniform case ( [1,2,5,6,16,22,24,[29][30][31]).…”

On Dichotomy With Differentiable Growth Rates for Skew-Evolution Cocycles in Banach Spaces

“…The polynomial case was introduced by Barreira and Valls in [1] and it was also studied by Boruga (Toma) and Megan [3,4,5], Megan and Stoica [12], Rȃmneant ¸u, Ceauşu and Megan [17].…”