Search results for "hyperbolic"
showing 6 items of 156 documents
Towards a global view of dynamical systems, for the C1-topology.
2010
This paper suggests a program for getting a global view of the dynamics of diffeomorphisms, from the point of view of the C1-topology. More precisely, given any compact manifold M, one splits Diff1(M) in disjoint C1-open regions whose union is C1-dense, and conjectures state that these open set, and their complement, are characterized by the presence of • either a robust local phenomenon • or a global structure forbiding this local phenomenon. Other conjectures states that some of these regions are empty. This set of conjectures draws a global view of the dynamics, putting in evidence the coherence of the numerous recent results on C1-generic dynamics.
Broglie and Young, visionaries who shed light in the polar topology that grounds our reality: a hypothesis
2020
Una observación matemática que relaciona los patrones fractales y la operación de convolución en el contexto del procesamiento de imágenes digitales interrumpió una investigación que nos lleva a plantear la hipótesis de que el concepto de onda de materia (o dualidad onda-partícula) se encuentra en la dicotomía entre el par débil y un topología fuerte en el ámbito del marco de atractores singulares continuos en ninguna parte diferenciables y el concepto de fotón-solitón de Vigier. Tal inferencia parece ser más evidente en la interpretación de Broglie-Bohm de la mecánica cuántica en el cruce de características locales x globales. De esto se deduce también que la relación de los fenómenos natu…
Semi-discrete Galerkin approximation method applied to initial boundary value problems for Maxwell's equations in anisotropic, inhomogeneous media
1981
SynopsisIn this paper the semi-discrete Galerkin approximation of initial boundary value problems for Maxwell's equations is analysed. For the electric field a hyperbolic system of equations is first derived. The standard Galerkin method is applied to this system and a priori error estimates are established for the approximation.
Functional inequalities for generalized inverse trigonometric and hyperbolic functions
2014
Various miscellaneous functional inequalities are deduced for the so-called generalized inverse trigonometric and hyperbolic functions. For instance, functional inequalities for sums, difference and quotient of generalized inverse trigonometric and hyperbolic functions are given, as well as some Gr\"unbaum inequalities with the aid of the classical Bernoulli inequality. Moreover, by means of certain already derived bounds, bilateral bounding inequalities are obtained for the generalized hypergeometric ${}_3F_2$ Clausen function.
Vegetation Patterns in the Hyperbolic Klausmeier Model with Secondary Seed Dispersal
2023
This work focuses on the dynamics of vegetation stripes in sloped semi-arid environments in the presence of secondary seed dispersal and inertial effects. To this aim, a hyperbolic generalization of the Klausmeier model that encloses the advective downhill transport of plant biomass is taken into account. Analytical investigations were performed to deduce the wave and Turing instability loci at which oscillatory and stationary vegetation patterns arise, respectively. Additional information on the possibility of predicting a null-migrating behavior was extracted with suitable approximations of the dispersion relation. Numerical simulations were also carried out to corroborate theoretical pre…
Oscillatory periodic pattern dynamics in hyperbolic reaction-advection-diffusion models
2022
In this work we consider a quite general class of two-species hyperbolic reaction-advection-diffusion system with the main aim of elucidating the role played by inertial effects in the dynamics of oscillatory periodic patterns. To this aim, first, we use linear stability analysis techniques to deduce the conditions under which wave (or oscillatory Turing) instability takes place. Then, we apply multiple-scale weakly nonlinear analysis to determine the equation which rules the spatiotemporal evolution of pattern amplitude close to criticality. This investigation leads to a cubic complex Ginzburg-Landau (CCGL) equation which, owing to the functional dependence of the coefficients here involve…