Sentence examples for exponential contraction from inspiring English sources

We recall the notion of a ρ-nonuniform exponential contraction.

Assume that (1) admits a ρ-nonuniform exponential contraction and (H1 - H3) hold.

We also show that the constants determining the nonuniform exponential contraction or nonuniform exponential dichotomy vary continuously with the perturbation.

We also consider the case of exponential contraction and show that the asymptotic stability persists under sufficiently small nonlinear perturbations.

Solutions of (1) are characterised by fast transitions between, followed by exponential contraction onto the slow manifolds.

Using exponential contraction, we establish an upper bound for the Morse lemma that is optimal up to multiplicative constants, which we demonstrate by presenting a concrete example.

We construct topological conjugacies between linear and nonlinear evolution operators that admit either a nonuniform exponential contraction or a nonuniform exponential dichotomy.

In Section 2, we show that the asymptotic stability of a ρ-nonuniform exponential contraction persists under sufficiently small nonlinear perturbations.

In this section, we show that the asymptotic stability of a ρ-nonuniform exponential contraction persists under sufficiently small nonlinear perturbations.

We also consider the case of exponential contractions, which allow a simpler treatment, and we show that they persist under sufficiently small nonlinear perturbations.

Exponential growth followed by a contraction phase can be fitted by a multitude of models.