Searcharxiv⌕ Search

arXiv subjects

Fernando Oliveira

Publications and source records attributed to Fernando Oliveira.

8 recordsLinked to original sources
arXiv2024

Positive topological entropy for the Standard Map

We show that for the standard map family, for all values of the parameter, except one, the mapping has positive topological entropy. The main tool is the following result. Let $S$ be a compact connected orientable surface and $f:S \rightarrow S$ an area preserving orientation preserving $C \e 1$ diffeomorphism of $S$. Assume that $U$ is an invariant domain of $S$ such that $fr_S{U}$ has a finite number of connected components. Let $b$ be a regular ideal boundary point of $U$ which is fixed under the induced action by $f$ on the ideal boundary of $U$, and let $\hat{f}:C(b) \rightarrow C(b)$ the homeomorphism on the corresponding circle of prime ends. Let $Z(b)$ be the impression of $b$ in $S$ and assume that all fixed points of $f$ in $Z(b)$ are non degenerate. If there exists a fixed prime end $e \in C(b)$ then we know the following. $\left(1\right)$ If $p$ is the principal point of $e$ then $p$ is also a fixed point of $Z(b)$ and $p$ is a saddle. $\left(2\right)$ $C(b)$ has a finite number of fixed prime ends and there exists a finite singular covering $ \phi :C(b) \rightarrow Z(b)$, which is a semiconjugacy between the mapping of prime ends on $C(b)$ and the restriction of $f$ to $Z(b)$. In particular, $Z(b)$ is the connected union of finitely many saddle connections and the corresponding saddles. This can be seen as a two dimensional generalization of the dynamics of homeomorphisms of the circle with fixed points.

math.DS↗
arXiv2023

Non-commutative gauge symmetry from strong homotopy algebras

We explicitly construct an L$_\infty$ algebra that defines U$_{\star}(1)$ gauge transformations on a space with an arbitrary non-commutative and even non-associative star product. Matter fields are naturally incorporated in this scheme as L$_\infty$ modules. Some possibilities for including P$_\infty$ algebras are also discussed.

hep-th↗
arXiv2022

The ideal boundary and the accumulation lemma

Let $S$ be a connected surface possibly with boundary, $\mu$ a finite Borel measure which is positive on open sets and $f:S\to S$ a homeomorphism preserving $\mu$. We prove that if $K$ is a compact connected subset of $S$ and $L$ is a branch of a hyperbolic periodic point if $f$ then $L\cap K\ne\emptyset$ implies $L\subset K$. This is called the accumulation lemma. For this we develop a classification of connected surfaces with boundary and a characterization of residual domains of compact subsets with finitely many connected components in a connected surface with boundary.

math.DS↗
arXiv2022

No elliptic points from fixed prime ends

We consider area preserving maps of surfaces and extend Mather's result on the equality of the closure of the four branches of saddles. He assumed elliptic fixed points to be Moser stable, while we require only that the derivative at this points to be a rotation by an angle different from zero. There are many results in the literature which require the hypothesis that elliptic periodic points be Moser stable that now can be extended to the case that the derivative at these points be an irrational rotation. The key point is to give more information on Cartwright and Littlewood's fixed point theorem, to show that the fixed point obtained by a fixed prime end can not be elliptic. Hypotheses then became easier to verify: non degeneracy of fixed points and nonexistence of saddle connections. As an application we show that the result immediately implies that for the standard map family, for all values of the parameter, except one, the principal hyperbolic fixed point has homoclinic points. We also extend results to surfaces with boundary in order to be applicable to return maps to surfaces of section and broken book decompositions.

math.DS↗
arXiv2020

Experimental Study on the Aerodynamic Sealing of Air Curtains

Controlling the air quality is of the utmost importance in today buildings. Vertical air curtains are often used to separate two different climatic zones with a view to reduce heat transfer. In fact, this research work proposes an air curtain aimed to ensure a proper separation between two zones, a clean one and a contaminated one. The methodology of this research includes: (i) small-scale tests on water models to ensure that the contamination does not pass through the air curtain, and (ii) an analytical development integrating the main physical characteristics of plane jets. In the solution developed, the airflow is extracted from the contaminated compartment to reduce the curtain airflow rejected to the exterior of the compartment. In this research work, it was possible to determine the minimum exhaust flow necessary to ensure the aerodynamic sealing of the air curtain. This article addresses the methodology used to perform the small-scale water tests and the corresponding results.

physics.flu-dyn↗
arXiv2016

On the Transitivity of Invariant Manifolds of Conservative Flows

The main result of this work is the following: for volume preserving flows on compact manifolds with the $C^r$ topology, $1 \leqq r \leqq \infty$ , the closure of every invariant manifold of periodic orbits and singularities is a chain transitive set. We also develop to new local constructions, which surprise by the simplicity of the arguments. One, a local perturbation to change an orbit to a nearby without altering its past. The other is a flow box theorem in the context of volume preserving flows, a result that is well known for Hamiltonians or general flows.

math.DS↗