We give bounds for the global attractor of the delay differential equation ẋ(t) = −μx(t) + f(x(t−τ)), where f is unimodal and has negative Schwarzian derivative. If f and μ satisfy certain condition, then, regardless of the delay, all solutions enter the domain where f is monotone decreasing and the powerful results for delayed monotone feedback can be applied to describe the asymptotic behavio...

We provide a detailed construction of the quantum theory massless scalar field on 2-dimensional, globally-hyperbolic (in particular, Lorentzian) manifolds using framework perturbative algebraic theory. From this we subalgebras observables isomorphic to Heisenberg and Virasoro algebras Einstein cylinder. also show how conformal version general covariance, as first introduced by Pinamonti an exte...

This note is a sequel to our paper [OS] where we generalized the Schwarzian derivative to conformal mappings of Riemannian manifolds. There we found that many of the phenomena familiar from the classical theory have counterparts in the more general setting. Here we advance this another step by giving a generalization of the well known univalence criterion of Nehari [N]. Despite its relatively a...

is the Schwarzian derivative of w =/(z). The two cases treated in [3 ] were m(\z\) =ir2/2 and m(\z\) =2(1 — \z\ 2)~2. The constants appearing in both criteria are the largest possible. In the first case this is shown by the existence of the nonunivalent function w = tan ir( 1 + e)z/2 (e>0) for which {w, z\ =7r2(l+e)2/2, and in the second case by an example constructed by E. Hille [2]. Other cri...

We prove that any C transformation, possibly with a (non-flat) critical or singular region, admits an invariant probability measure absolutely continuous with respect to any expanding measure whose Jacobian satisfies a mild distortion condition. This is an extension to arbitrary dimension of a famous theorem of Keller [37] for maps of the interval with negative Schwarzian derivative. We also sh...

We present a novel integrable non-autonomous partial differential equation of the Schwarzian type, i.e. invariant under Möbius transformations, that is related to the Korteweg-de Vries hierarchy. In fact, this PDE can be considered as the generating equation for the entire hierarchy of Schwarzian KdV equations. We present its Lax pair, establish its connection with the SKdV hierarchy, its Miura...

A bstract We attempt to understand the CFT 1 structure underlying (2+1)D gravity in flat spacetime via dimensional reduction. observe that under superrotation, hyperbolic (and dS 2 ) slices of transform asymptotically (A)dS slices. consider a wedge region bounded by two such surfaces as End-of-the-World branes and employ Wedge holography perform holographic show once we fluctuating branes, loca...

Many integrable hierarchies of differential equations allow a variational description, called Lagrangian multiform or pluri-Lagrangian structure. The fundamental object in this theory is not Lagrange function but $d$-form that integrated over arbitrary $d$-dimensional submanifolds. All such action integrals must be stationary for field to solution the problem. In paper we present procedure obta...