We derive a numerical scheme to compute invariant manifolds for timevariant discrete dynamical systems, i.e., nonautonomous difference equations. Our universally applicable method is based on a truncated Lyapunov-Perron operator and computes invariant manifolds using a system of nonlinear algebraic equations which can be solved both locally using (nonsmooth) inexact Newton, and globally using c...

Abstract. We study decay of correlations, the asymptotic distribution of hitting times and fluctuations of the return times for a robust class of multidimensional non-uniformly hyperbolic transformations. Oliveira and Viana [15] proved that there is a unique equilibrium state μ for a large class of nonuniformly expanding transformations and Hölder continuous potentials with small variation. For...

Several types of differential equations, such as delay differential equations, age-structure models in population dynamics, evolution equations with boundary conditions, can be written as semilinear Cauchy problems with an operator which is not densely defined in its domain. The goal of this paper is to develop a center manifold theory for semilinear Cauchy problems with non-dense domain. Using...

Dynamics of deterministic systems perturbed by random additive noise is characterized quantitatively. Since for such systems the Kolmogorov-Sinai (KS) entropy diverges if the diameter of the partition tends to zero, we analyze the difference between the total entropy of a noisy system and the entropy of the noise itself. We show that this quantity is finite and non-negative and we call it the d...

The study of transport and mixing processes in dynamical systems is particularly important for the analysis of mathematical models of physical systems. Barriers to transport, which mitigate mixing, are currently the subject of intense study. In the autonomous setting, the use of transfer operators (Perron–Frobenius operators) to identify invariant and almost-invariant sets has been particularly...

Cauchy problem, 19, 136Condition number, 40, 55, 99, 110Contractibility, 183Counterflow equation, 156Critical delay, 167Delay Liapunov function, 138Delay margin, 170Departure from normality, 56Diagonalizable matrix, 55Diagonally dominant matrix, 36Differential inclusion, 45Dissipativity radius, 33Dual norm, 8, 25Dual pair, 25Eccentricity, ...

Keywords: Delay equations Exponential stability Oscillating coefficient Bohl–Perron type theorem a b s t r a c t New explicit exponential stability conditions are obtained for the nonautonomous linear equation ˙ x(t) + a(t)x(h(t)) = 0, where h(t) ≤ t and a(t) is an oscillating function. We apply the comparison method based on the Bohl–Perron type theorem. Coefficients and delays are not assumed...