A dynamical system is called contractive if any two solutions approach one another at an exponential rate. More precisely, the dynamics contracts lines This property implies highly ordered asymptotic behavior including entrainment to time-varying periodic vector fields and, in particular, global stability for time-invariant fields. Contraction theory has found numerous applications systems and ...

In this report, we analyze the asymptotic efficiency of self-adjusting contraction trees proposed as part of the Slider project [2, 3]. Self-adjusting contraction trees are used for incremental computation [1, 4, 5, 8]. Our analysis extends the asymptotic efficiency analysis of Incoop [6, 7]. We consider two different runs: the initial run of an Slider computation, where we perform a computatio...

A bstract Asymptotic symmetries in Carrollian gravitational theories 3+1 space and time dimensions obtained from “magnetic” “electric” ultrarelativistic contractions of General Relativity are analyzed. In both cases, parity conditions needed to guarantee a finite symplectic term, analogy with Einstein gravity. For the magnetic contraction, when Regge-Teitelboim imposed, asymptotic described by ...

Asymptotic couples (of H-type) try to capture the structure induced by the derivation of a Hardy field K on the value group of the natural valuation on K. In this note we continue the study of algebraic and model-theoretic aspects of asymptotic couples undertaken in [1]. We give a short exposition of some basic facts about asymptotic couples, and address a few topics left out in that paper: the...

Abstract Using the notion of strict h-contraction, existence results for Ψ-asymptotic equivalence two pairs (Lyapunov) matrix differential equations with integral term as right side and modified argument are given.

In the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ isgiven where $sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applic...