arXiv subjects

Suzete M. Afonso

Publications and source records attributed to Suzete M. Afonso.

3 recordsLinked to original sources

arXiv2021

Equilibrium states for non-uniformly hyperbolic systems: statistical properties and analyticity

We consider a wide family of non-uniformly expanding maps and hyperbolic Hölder continuous potentials. We prove that the unique equilibrium state associated to each element of this family is given by the eigenfunction of the transfer operator and the eigenmeasure of the dual operator (both having the spectral radius as eigenvalue). We show that the transfer operator has the spectral gap property in some space of Hölder continuous observables and from this we obtain an exponential decay of correlations and a central limit theorem for the equilibrium state. Moreover, we establish the analyticity with respect to the potential of the equilibrium state as well as that of other thermodynamic quantities. Furthermore, we derive similar results for the equilibrium state associated to a family of non-uniformly hyperbolic skew products and hyperbolic Hölder continuous potentials.

math.DS↗

arXiv2018

Existence, uniqueness, and approximation for solutions of a functional-integral equation in $L^p$ spaces

In this work we consider the general functional-integral equation: \begin{equation*} y(t) = f\left(t, \int_{a}^{b} k(t,s)g(s,y(s))ds\right), \qquad t\in [a,b], \end{equation*} and give conditions that guarantee existence and uniqueness of solution in $L^p([a,b])$, with $1<p<\infty$. We use Banach Fixed Point Theorem} and employ the successive approximation method and Chebyshev quadrature for approximating the values of integrals. Finally, to illustrate the results of this work, we provide some numerical examples.

math.NA↗

arXiv2018

Existence of periodic solution for a class of neutral differential equations with impulses

By applying a Mawhin's continuation theorem of coincidence degree theory, we establish sufficient conditions for the existence of a periodic solution for a class of impulsive neutral differential equations. The procedure adopted in this work makes use of a non-impulsive associated equation in order to overcome the difficulties resulting from the moments of impulse effects. Under particular assumptions this solution is continuously differentiable on each interval with no impulse effect.

math.CA↗