Results 11 to 20 of about 7,827 (246)

Lyapunov functions for strong exponential dichotomies

Journal of Mathematical Analysis and Applications, 2013
We give a complete characterization of a general type of exponential dichotomies in terms of Lyapunov functions, both for discrete and continuous time. This includes constructing explicitly quadratic Lyapunov functions for each exponential dichotomy.
Barreira, Luis, Dragičević, Davor, Valls, Claudia   +2 more
openaire   +6 more sources

Strong and weak admissibility of $L^\infty$ spaces

Electronic Journal of Qualitative Theory of Differential Equations, 2017
For a dynamics with continuous time, we consider the notion of a strong exponential dichotomy with respect to a family of norms and we characterize it in terms of the admissibility of bounded solutions.
Luis Barreira, Claudia Valls
doaj   +1 more source

On Roughness of Exponential Dichotomy

Journal of Mathematical Analysis and Applications, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ju, Ning, Wiggins, Stephen
openaire   +2 more sources

Exponential Dichotomies and Fredholm Operators [PDF]

Proceedings of the American Mathematical Society, 1988
It is shown that if the operator ( L x ) ( t ) = x ˙ ( t ) − A ( t ) x (
openaire   +1 more source

Holder Shadowing on Finite Intervals [PDF]

, 2013
For any $\theta, \omega > 1/2$ we prove that, if any $d$-pseudotrajectory of length $\sim 1/d^{\omega}$ of a diffeomorphism $f\in C^2$ can be $d^{\theta}$-shadowed by an exact trajectory, then $f$ is structurally stable.
Anosov, Koropecki, Maizel, Pliss, SERGEY TIKHOMIROV, Yu Pilyugin   +5 more
core   +1 more source

Stability of Traveling Waves Based upon the Evans Function and Legendre Polynomials

Applied Sciences, 2020
One of the tools and techniques concerned with the stability of nonlinear waves is the Evans function which is an analytic function whose zeros give the eigenvalues of the linearized operator.
H. M. Srivastava, H. I. Abdel-Gawad, Khaled M. Saad   +2 more
doaj   +1 more source

Tempered exponential behavior for a dynamics in upper triangular form

Electronic Journal of Qualitative Theory of Differential Equations, 2018
We consider the problem of whether the existence of a tempered exponential dichotomy for a linear dynamics can be deduced from the same property for the dynamics restricted to each diagonal entry.
Luis Barreira, Claudia Valls
doaj   +1 more source

Non-Atkinson perturbations of nonautonomous linear Hamiltonian systems: exponential dichotomy and nonoscillation [PDF]

, 2017
Producción CientíficaWe analyze the presence of exponential dichotomy (ED) and of global existence of Weyl functions $M^\pm$ for one-parametric families of finite-dimensional nonautonomous linear Hamiltonian systems defined along the orbits of a compact ...
Núñez Jiménez, María del Carmen, Obaya García, Rafael   +1 more
core   +3 more sources

Exponential dichotomies and transversal homoclinic points

Physica D: Nonlinear Phenomena, 1984
Kenneth J Palmer
exaly   +5 more sources

Exact Boundary Conditions at an Artificial Boundary for Partial Differential Equations in Cylinders [PDF]

, 1986
The numerical solution of partial differential equations in unbounded domains requires a finite computational domain. Often one obtains a finite domain by introducing an artificial boundary and imposing boundary conditions there. This paper derives exact
Hagstrom, Thomas, Keller, H. B.
core   +1 more source