Search results for "Mathematical analysis"

Periodic and quasi-periodic orbits of the dissipative standard map

2011

We present analytical and numerical investigations of the dynamics of the dissipative standard map. We first study the existence of periodic orbits by using a constructive version of the implicit function theorem; then, we introduce a parametric representation, which provides the interval of the drift parameter ensuring the existence of a periodic orbit with a given period. The determination of quasi--periodic attractors is efficiently obtained using the parametric representation combined with a Newton's procedure, aimed to reduce the error of the approximate solution provided by the parametric representation. These methods allow us to relate the drift parameter of the periodic orbits to th…

Mappings of finite distortion: Removable singularities for locally homeomorphic mappings

2004

Let f be a locally homeomorphic mapping of finite distortion in dimension larger than two. We show that when the distortion of f satisfies a certain subexponential integrability condition, small sets are removable. The smallness is measured by a weighted modulus.

Mappings of finite distortion: Removable singularities

2003

We show that certain small sets are removable for bounded mappings of finite distortion for which the distortion function satisfies a suitable subexponential integrability condition. We also give an example demonstrating the sharpness of this condition.

Mappings of finite distortion: The Rickman-Picard theorem for mappings of finite lower order

2004

We show that an entire mappingf of finite distortion with finite lower order can omit at most finitely many points when the distortion function off is suitably controlled. The proof uses the recently established modulus inequalities for mappings of finite distortion [15] and comparison inequalities for the averages of the counting function. A similar technique also gives growth estimates for mappings having asymptotic values.

Mappings of finite distortion and asymmetry of domains

2013

We establish an anisotropic Bonnesen inequality for images of balls under homeomorphisms with exponentially integrable distortion. Mathematics Subject Classification (2000): 30C65, 46E35.

Quasiconformal distortion on arcs

1994

Generalized dimension distortion under planar Sobolev homeomorphisms

2009

We prove essentially sharp dimension distortion estimates for planar Sobolev-Orlicz homeomorphisms.

Mappings of finite distortion: decay of the Jacobian in the plane

2008

A contribution to solve the problem of attributing harmonic distortion responsibility

2005

Owing to the proliferation of loads which draw nonsinusoidal currents, the current and voltage distortion in distribution systems is ever increasing. The correct identification of the source of distortion is important for attributing the responsibility of disturbances to utility and customers. In this paper, a new classification of the possible classes of responsibility is proposed, defining some conditions, based on the improvement of the method of decomposition of the current into conforming and nonconforming components, and of the method based on the evaluation of the sign of harmonic active powers, which allows their identification.

Localization and separation of solutions for Fredholm integral equations

2020

[EN] In this paper, we establish a qualitative study of nonlinear Fredholm integral equations, where we will carry out a study on the localization and separation of solutions. Moreover, we consider an efficient algorithm to approximate a solution. To do this, we study the semilocal convergence of an efficient third order iterative scheme for solving nonlinear Fredholm integral equations under mild conditions. The novelty of our work lies in the fact that this study involves first order Frechet derivative and mild conditions. A numerical example involving nonlinear Fredholm integral equations, is solved to show the domains of existence and uniqueness of solutions. The applicability of the it…