Hyperbolic discount functions induce dynamically inconsistent preferences, implying a motive for consumers to constrain their own future choices. This paper analyzes the decisions of a hyperbolic consumer who has access to an imperfect commitment technology: an illiquid asset whose sale must be initiated one period before the sale proceeds are received. The model predicts that consumption track...

The double torus provides a relativistic model for a closed 2D cosmos with topology of genus 2 and constant negative curvature. Its unfolding into an octagon extends to an octagonal tesselation of its universal covering, the hyperbolic space H. The tesselation is analysed with tools from hyperbolic crystallography. Actions on H of groups/subgroups are identified for SU(1, 1), for a hyperbolic C...

The double torus provides a relativistic model for a closed 2D cosmos with topology of genus 2 and constant negative curvature. Its unfolding into an octagon extends to an octagonal tesselation of its universal covering, the hyperbolic space H. The tesselation is analysed with tools from hyperbolic crystallography. Actions on H of groups/subgroups are identified for SU(1, 1), for a hyperbolic C...

Hyperbolic systems of dissipative type, contracting the phase space volume, manifest robust attractors. There are several classes of discrete time systems which produce hyperbolic nontrivial attractor – like the Plykin attractors [P] or the Smale attractors [KH]. Recently, Kuznetsov [K] proposed a continuous model for which there is a good numerical evidence of the existence of an uniformly hyp...

In this paper, we prove some fixed points properties and demiclosedness principle for a Banach operator in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a fixed point of a Banach operator and establish some strong and $Delta$-convergence theorems for such operator in the frame work of uniformly convex hyperbolic spaces. The results obtained in this...

‎In this paper we characterize Bergman spaces with‎ ‎respect to double integral of the functions $|f(z)‎ ‎-f(w)|/|z-w|$,‎ ‎$|f(z)‎ -‎f(w)|/rho(z,w)$ and $|f(z)‎ ‎-f(w)|/beta(z,w)$,‎ ‎where $rho$ and $beta$ are the pseudo-hyperbolic and hyperbolic metrics‎. ‎We prove some necessary and sufficient conditions that implies a function to be...

This paper deals with the regulation problem of a class of irrigation canals using the Saint-Venant partial differential equations (pde). The Internal Model Boundary Control (IMBC) approach is used and the multireaches case is considered (several reaches in cascade). Perturbation theory of exponential semigroup used for control synthesis is extended here to nonhomogeneous hyperbolic systems, as...

This paper describes a very general absorbing layer model for hyperbolic-parabolic systems of partial differential equations. For linear systems with constant coefficients it is shown that the model possesses the perfect matching property, i.e., it is a perfectly matched layer (PML). The model is applied to two linear systems: a linear wave equation with a viscous damping term and the linearize...

We consider the matrix model associated with pp-wave background and construct supersymmetric branes. In addition to the spherical membrane preserving 16 supersymmetries, one may construct rotating elliptic membranes preserving 8 supersymmetries. The other branch describes rotating 1/8 BPS hyperbolic branes in general. When the angular momentum vanishes, the hyperbolic brane becomes 1/4 BPS pres...

We study the neural field equations introduced by Chossat and Faugeras to model the representation and the processing of image edges and textures in the hypercolumns of the cortical area V1. The key entity, the structure tensor, intrinsically lives in a non-Euclidean, in effect hyperbolic, space. Its spatio-temporal behaviour is governed by nonlinear integro-differential equations defined on th...