Stable weakly shadowable volume-preserving systems are volume-hyperbolic

We prove that any C1-stable weakly shadowable volume-preserving diffeomorphism defined on a compact manifold displays a dominated splitting E ⊕ F. Moreover, both E and F are volume-hyperbolic. Finally, we prove the version of this result for divergence-free vector fields. As a consequence, in low dimensions, we obtain global hyperbolicity.     

Sliding Mode Control of a Remotely Operated Underwater Vehicle with Adaptive Fuzzy Dead-Zone Compensation

Due to the great technological improvement obtained in the last decades, it became possible to use robotic vehicles for underwater exploration. During the execution of a certain task with a remotely operated underwater vehicle, the operator needs to monitor and control a number of parameters. If some of these parameters, as for instance position and attitude, could be controlled automatically, the teleoperation of the vehicle can be enormously facilitated. Based on experimental tests, it was verified that marine thrusters can exhibit dead-zone nonlinearities. This work describes the development of a variable structure control strategy for an underwater vehicle with a thrust system subject to dead-zone input. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Generic Hamiltonian Dynamics

In this paper we contribute to the generic theory of Hamiltonians by proving that there is a \(C^2\)-residual \({\mathcal {R}}\) in the set of \(C^2\) Hamiltonians on a closed symplectic manifold \(M\), such that, for any \(H\in {\mathcal {R}}\), there is a full measure subset of energies \(e\) in \(H(M)\) such that the Hamiltonian level \((H,e)\) is topologically mixing; moreover these level sets are homoclinic classes.     

A Review of Multiple Scale Fibrous and Composite Systems for Heating Applications

Different types of heating systems have been developed lately, representing a growing interest in both the academic and industrial sectors. Based on the Joule effect, fibrous structures can produce heat once an electrical current is passed, whereby different approaches have been followed. For that purpose, materials with electrical and thermal conductivity have been explored, such as carbon-based nanomaterials, metallic nanostructures, intrinsically conducting polymers, fibers or hybrids. We review the usage of these emerging nanomaterials at the nanoscale and processed up to the macroscale to create heaters. In addition to fibrous systems, the creation of composite systems for electrical and thermal conductivity enhancement has also been highly studied. Different techniques can be used to create thin film heaters or heating textiles, as opposed to the conventional textile technologies. The combination of nanoscale and microscale materials gives the best heating performances, and some applications have already been proven, even though some effort is still needed to reach the industry level.     

On the nucleation of hadronic domains in the quark-hadron transition

We present numerical results on bubble profiles, nucleation rates and time evolution for a weakly first-order quark-hadron phase transition in different expansion scenarios. We confirm the standard picture of a cosmological first-order phase transition, in which the phase transition is entirely dominated by nucleation. We also show that, even for expansion rates much lower than those expected in heavy-ion collisions nucleation is very unlikely, indicating that the main phase conversion mechanism is spinodal decomposition.     

Topological stability for conservative systems

We prove that the C¹ interior of the set of all topologically stable C¹ incompressible flows is contained in the set of Anosov incompressible flows. Moreover, we obtain an analogous result for the discrete-time case.     

An extension of Barta’s Theorem and geometric applications

We prove an extension of a theorem of Barta and we give some geometric applications. We extend Cheng’s lower eigenvalue estimates of normal geodesic balls. We generalize Cheng-Li-Yau eigenvalue estimates of minimal submanifolds of the space forms. We show that the spectrum of the Nadirashvili bounded minimal surfaces in have positive lower bounds. We prove a stability theorem for minimal hypersurfaces of the Euclidean space, giving a converse statement of a result of Schoen. Finally we prove generalization of a result of Kazdan–Kramer about existence of solutions of certain quasi-linear elliptic equations. Bessa and Montenegro were partially supported by CNPq Grant.     

Straighten out coordinates for volume-preserving actions

Archiv der Mathematik - In this short note we obtain a canonical form for commuting divergence-free vector fields.