nonuniform hyperbolicity
Recently Published Documents


TOTAL DOCUMENTS

30
(FIVE YEARS 2)

H-INDEX

9
(FIVE YEARS 0)

2021 ◽  
pp. 1-27
Author(s):  
Tomás Caraballo ◽  
Alexandre N. Carvalho ◽  
José A. Langa ◽  
Alexandre N. Oliveira-Sousa

In this paper, we study stability properties of nonuniform hyperbolicity for evolution processes associated with differential equations in Banach spaces. We prove a robustness result of nonuniform hyperbolicity for linear evolution processes, that is, we show that the property of admitting a nonuniform exponential dichotomy is stable under perturbation. Moreover, we provide conditions to obtain uniqueness and continuous dependence of projections associated with nonuniform exponential dichotomies. We also present an example of evolution process in a Banach space that admits nonuniform exponential dichotomy and study the permanence of the nonuniform hyperbolicity under perturbation. Finally, we prove persistence of nonuniform hyperbolic solutions for nonlinear evolution processes under perturbations.


2020 ◽  
Vol 358 (3) ◽  
pp. 341-364
Author(s):  
Mengmeng Li ◽  
JinRong Wang ◽  
Donal O’Regan ◽  
Michal Fečkan

2019 ◽  
Vol 266 (4) ◽  
pp. 2175-2213
Author(s):  
Luis Barreira ◽  
Claudia Valls

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Muna Abu Alhalawa ◽  
Davor Dragičević

We give a complete functional theoretic characterization of tempered exponential dichotomies in terms of the invertibility of certain linear operators acting on a suitable Frechét space. In sharp contrast to previous results, we consider noninvertible linear cocycles acting on infinite-dimensional spaces. The principal advantage of our results is that they avoid the use of Lyapunov norms.


2016 ◽  
Vol 27 (2) ◽  
pp. 235-247 ◽  
Author(s):  
Luis Barreira ◽  
Davor Dragičević ◽  
Claudia Valls

2015 ◽  
Vol 64 (6) ◽  
pp. 1124-1144 ◽  
Author(s):  
Luis Barreira ◽  
Claudia Valls

2014 ◽  
Vol 14 (3) ◽  
Author(s):  
Luis Barreira ◽  
Claudia Valls ◽  
Davor Dragičevič

AbstractFor a nonautonomous dynamics defined by a sequence of linear operators, we consider the notion of an exponential dichotomy with respect to a sequence of norms and we characterize it completely in terms of the admissibility in pairs of spaces (ℓ


Sign in / Sign up

Export Citation Format

Share Document