Encontrados 9 documentos, a visualizar página 1 de 1
Geodesic length spectrum on compact Riemann surfaces
Gracio, Clara; Ramos, José SousaIn this paper we use techniques linking combinatorial structures (symbolic dynamics) and algebraic-geometric structures to study the variation of the geodesic length spectrum, with the Fenchel-Nielsen coordinates, which parametrize the surface of genus τ = 2. We explicitly compute length spectra, for all closed orientable hyperbolic genus two surfaces, identifying the exponential growth rate and the first terms...
LAPLACIANS AND THE CHEEGER CONSTANTS FOR DISCRETE DYNAMICAL SYSTEMS
Gracio, Clara; Fernandes, Sara; Ramos, José SousaWe consider discrete laplacians for iterated maps on the interval and examine their eigenvalues. We have introduced a notion of conductance (Cheeger constant) for a discrete dynamical system, now we study their relations with the spectrum. We compute the systoles and the first eigenvalue of some families of discrete dynamical systems.
Chaotic behavior in a two--dimensional business cycle model
Grácio, Clara; Januário, Cristina; Ramos, José SousaWe consider a discrete-time economic model which is a particular case of the Kaldor-type business cycle model and it is described by a two-dimensional dynamical system. Under certain conditions the map can be reduced to a skew map whose components, the base and the fiber map, both have entropy. Our proposal is to study and measure the complexity of the system using symbolic dynamics techniques and the topologic...
Symbolic Spectrum of the Laplacian on hyperbolic surfaces
Gracio, Clara; Ramos, José SousaOur main tool is a method for studying how the hyperbolic metric on a Riemann surface behaves under deformation of the surface. We study the variation of the rst eigenvalue of the Laplacian and the conductance of the dynamical system, with the Fenchel-Nielsen coordinates, that parameterizes the surface.
The first eigenvalue of the Laplacian and the Conductance of a Compact surface
Gracio, Clara; Ramos, José SousaWe present some results with the central theme of is the phenomenon of the first eigenvalue of the Laplacian and conductance of the dynamical system. Our main tool is a method for studying how the hyperbolic metric on a Riemann surface behaves under deformation of the surface. With this model, we show variation of the first eigenvalue of the laplacian and the conductance of the dynamical system, with the Fenche...
Chaotic behavior in an economic model
Gracio, Clara; Januario, Cristina; Ramos, José SousaThe purpose of this work is to study a discrete-time nonlinear business cycle model of the Kaldor-type. The model is an extended Kaldor model and it is described by a two-dimensional dynamical system with income and capital as variables. We check the orbits of the system, their changes related to changes of the system parameters and their basins of attraction in order to understand the dynamic features of the m...
Rigidity and flexibility of surface groups
Gracio, Clara; Ramos, José SousaThe aim of this work is the °exibility of the hyperbolic surfaces. The results are about °exibility and geometrical boundedness. Bers are stated the universal property for all hyperbolic surface of ¯nite area where introduced the constant of boundedness. We determine this constant, using symbolic dynamics.
The first eigenvalue of the Laplacian and the ground flow of a compact surface
Gracio, Clara; Ramos, José SousaWe present some results whose central theme is that the phenomenon of the first eigenvalue of the Laplacian and the ground flow of the compact surface (bitorus). Our main tool is a method for studying how the hyperbolic metric on a Riemann surface behaves under deformation of the surface. With this model, we show that there are variation of the first eigenvalue of the Laplacian and the ground flow with the Fenc...
Boundary maps and Fenchel-Nielsen coordinates
Gracio, Clara; Ramos, José SousaWe consider a genus $2$ surface, $M$, of constant negative curvature and we construct a $12$-sided fundamental domain, where the sides are segments of the lifts of closed geodesics on $M$ (which determines the Fenchel-Nielsen-Maskit coordinates). Then we study the linear fractional transformations of the side pairing of the fundamental domain. This construction gives rise to $24$ distinct points on the bounda...
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