Related papers: Necessary and sufficient conditions for $a$-contra…
We offer a measure-theoretic extension of the concept and theory of $k$-contraction, including their generalization on fractional dimensions $d$. The respective contraction property is defined through the exponential decay of the…
Under a mild condition we give closed-form expressions for copulas of systems that consist of maxima and of minima of subvectors of a given random vector $X$ with continuous marginals. Said expressions appear explicit in the copula of $X$…
We obtain conditions for the existence and stability of de Sitter attractors in the phase space of spatially homogeneous and isotropic cosmology in generalized theories of gravity (including non-linear and scalar-tensor theories). These…
We study the shift of the chiral condensate in a constant electromagnetic field in the context of chiral perturbation theory. Using the Schwinger proper-time formalism, we derive a one-loop expression correct to all orders in $m_{\pi}^2 /…
In this short note we prove a hierarchical stability result that applies to hybrid dynamical systems satisfying the hybrid basic conditions of (Goebel et al., 2012). In particular, we establish sufficient conditions for uniform asymptotic…
In this paper, we derive differential conditions guaranteeing the orbital stability of nonlinear hybrid limit cycles. These conditions are represented as a series of pointwise linear matrix inequalities (LMI), enabling the search for…
Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability…
We consider a Lorentz-violating theory of inflation consisting of Einstein-aether theory with a scalar inflaton coupled bilinearly to the expansion of the aether. We determine the conditions for linearized stability, positive energy, and…
The union-closed sets conjecture (sometimes referred to as Frankl's conjecture) states that every finite, nontrivial union-closed family of sets has an element that is in at least half of its members. Although the conjecture is known to be…
We study the equivalence of two - order-by-order Einstein's equation and Reduced action - approaches to cosmological perturbation theory at all orders for different models of inflation. We point out a crucial consistency check which we…
In this work, we leverage the 2-contraction theory, which extends the capabilities of classical contraction theory, to develop a global stability framework. Coupled with powerful geometric tools such as the Poincare index theory, the…
This paper investigates contraction properties of switched dynamical systems for the case that all modes are non-contracting, thereby extending existing results that require at least one mode to be contracting. Leveraging the property that…
Using Conley theory we show that local attractors remain (past) attractors under small non-autonomous perturbations. In particular, the attractors of the perturbed systems will have positive invariant neighborhoods and converge upper…
We address the Riemann and Cauchy problems for systems of $n$ conservation laws in $m$ unknowns which are subject to $m-n$ constraints ($m\geq n$). Such constrained systems generalize systems of conservation laws in standard form to include…
Contraction analysis is a stability theory for nonlinear systems where stability is defined incrementally between two arbitrary trajectories. It provides an alternative framework in which to study uncertain interconnections or systems with…
We derive a sufficient condition for $k$-contraction in a generalized Lurie system~(GLS), that is, the feedback connection of a nonlinear dynamical system and a memoryless nonlinear function. For $k=1$, this reduces to a sufficient…
We consider a planar viscous shock for a scalar viscous conservation law with a strictly convex flux in multi-dimensional setting, where the transversal direction is periodic. We first show the contraction property for any solutions…
We develop sufficient analytic conditions for conservativeness of non-sectorial perturbations of symmetric Dirichlet forms which can be represented through a carr\'e du champ on a locally compact separable metric space. These form an…
We prove the $l^2$ Decoupling Conjecture for compact hypersurfaces with positive definite second fundamental form and also for the cone. This has a wide range of important consequences. One of them is the validity of the Discrete…
In this work we consider companion conservation laws to general systems of conservation laws. We investigate sufficient regularity for weak solutions to satisfy companion laws, assuming the fluxes to be $C^{1,\gamma}$, $0<\gamma<1$,…