On the Dynamics of Induced Maps on the Space of Probability Measures

For the generic continuous map and for the generic homeomorphism of the Cantor space, we study the dynamics of the induced map on the space of probability measures, with emphasis on the notions of Li-Yorke chaos, topological entropy, equicontinuity, chain continuity, chain mixing, shadowing and recurrence. We also establish some results concerning induced maps that hold on arbitrary compact metric spaces.Comment: 23 page

Mean Li-Yorke chaos in Banach spaces

We investigate the notion of mean Li-Yorke chaos for operators on Banach spaces. We show that it differs from the notion of distributional chaos of type 2, contrary to what happens in the context of topological dynamics on compact metric spaces. We prove that an operator is mean Li-Yorke chaotic if and only if it has an absolutely mean irregular vector. As a consequence, absolutely Ces\`aro bounded operators are never mean Li-Yorke chaotic. Dense mean Li-Yorke chaos is shown to be equivalent to the existence of a dense (or residual) set of absolutely mean irregular vectors. As a consequence, every mean Li-Yorke chaotic operator is densely mean Li-Yorke chaotic on some infinite-dimensional closed invariant subspace. A (Dense) Mean Li-Yorke Chaos Criterion and a sufficient condition for the existence of a dense absolutely mean irregular manifold are also obtained. Moreover, we construct an example of an invertible hypercyclic operator $T$ such that every nonzero vector is absolutely mean irregular for both $T$ and $T^{-1}$. Several other examples are also presented. Finally, mean Li-Yorke chaos is also investigated for $C_0$-semigroups of operators on Banach spaces.Comment: 26 page

A note on the continuity of multilinear mappings in topological modules

In the present note, we obtain a criterion for the equicontinuity of families of multilinear mappings between topological modules. We also give an example which shows that the hypothesis imposed on the neighborhoods of zero is essential for the validity of our theorem

Li-Yorke Chaos for Composition Operators on LpL^p-Spaces

Li-Yorke chaos is a popular and well-studied notion of chaos. Several simple and useful characterizations of this notion of chaos in the setting of linear dynamics were obtained recently. In this note we show that even simpler and more useful characterizations of Li-Yorke chaos can be given in the special setting of composition operators on $L^p$ spaces. As a consequence we obtain a simple characterization of weighted shifts which are Li-Yorke chaotic. We give numerous examples to show that our results are sharp

On the structure of the neritic suprabenthic communities from the Portuguese continental margin

This work presents the investigations made on the neritic suprabenthic communities of the Portuguese margin (continental shelf and upper slope) exposed to seasonal upwelling. These communities were sampled during the AVEIRO-94 cruise at 5 sites located along an E-W bathymetric transect from 21 to 299 m depth using a suprabenthic sled with superposed nets. In the 0 to 100 cm water layer, the total densities ranged from 700.2 to 13591.7 ind. 100m(-2). During daytime, the motile fauna was mainly concentrated within the 0 to 50 cm water layer (76.2 to 97.2% of the total abundance). The night-time sample at the shallower site showed a more even distribution of the fauna in the near-bottom water layers (nocturnal migratory behaviour of some motile species). The Shannon diversity (H') values ranged from 1.84 to 3.54 for the shelf sites and increased at the upper slope site (4.15). Mysids and amphipods were generally dominant except for at the middle part of the shelf where the latter was replaced by euphausiids. The suprabenthic fauna off Aveiro was compared with similar data from the same bathymetric sampling levels off Arcachon (Bay of Biscay). Multivariate analysis showed that differences in faunal composition between the 2 geographic areas were smaller than depth-related variations within geographic areas. The results were discussed in relation to other suprabenthic communities from the northeastern Atlantic.Programa de Cooperação Oceanológica Luso-FrancesaJNICT/Embaixada de FrançaFrench CIRMAT-CNR

Experimental observation of weak non-Markovianity

Non-Markovianity has recently attracted large interest due to significant advances in its characterization and its exploitation for quantum information processing. However, up to now, only non-Markovian regimes featuring environment to system backflow of information (strong non-Markovianity) have been experimentally simulated. In this work, using an all-optical setup we simulate and observe the so-called weak non-Markovian dynamics. Through full process tomography, we experimentally demonstrate that the dynamics of a qubit can be non-Markovian despite an always increasing correlation between the system and its environment which, in our case, denotes no information backflow. We also show the transition from the weak to the strong regime by changing a single parameter in the environmental state, leading us to a better understanding of the fundamental features of non-Markovianity.Comment: v2: final versio

Estudo de polímeros por microscopia de força atômica.

A microscopia de varredura de força (MVF SFM "scanning force microscopy") também conhecida como microscopia de força atômica (MFA AFM "atomic force microscopy") tem sido utilizada largamente no estudo de polímeros (Jandt (1998), Schneider & Herrmann (2001) e Hodges (2002)), devido a sua capacidade de fornecer informações que não eram passíveis de se obter com o uso da microscopia eletrônica de varredura. Por conseguir obter imagens de superfície de materiais sob as mais variadas condições (ar, vácuo e em meio líquido) se tornou um dos equipamentos mais completos para estudo de materiais em micro e nano escalas. Apresenta várias vantagens em relação às microscopias eletrônica (ME) de varredura e eletrônica de transmissão, para estudo de polímeros, entre elas: dispensar o uso de vácuo ou de recobrimento da amostra, a possibilidade de se realizar medidas diretas de altura e rugosidade, além de, para estruturas ordenadas, poder obter imagens com resolução atômica. As imagens obtidas com os diferentes tipos de AFM são relacionadas com a natureza das forças envolvidas: repulsão coulômbica (AFM -modo contato), força de van der Waals (AFM modo não contato e contato intermitente) (Meyer, 1992), força magnética (MFM), força elétrica (MFE), força de atrito entre outras (Jandt, 1998).bitstream/CNPDIA/8722/1/CT53_2003.pd

Caracterización química y mineral ógica de los sedimentos de los canales de Mira, Ílhavo y Ovar de la Laguna de Aveiro (Portugal)

The paleoenvironmental reconstruction of Aveiro Lagoon is being carried out based on the sedimentological, paleoecological, geochemical and mineralogical characterization of sediment samples collected systematically in the lagoon. This paper presents results concerning the changes in the chemical and mineralogical composition of the fine fraction (<63 μm) and the clay fraction (<2 μm) in sediment samples from Aveiro Lagoon, mainly collected from the lower intertidal plain and subtidal deposits located along the Mira, Ílhavo and Ovar channels. A zonography of the lagoon was established based on the parameters analyzed. The results show that the surface and near-surface sediments of Aveiro Lagoon trap relatively large quantities of trace metals, such as Cu, Pb, Co, Ni, Cd, Zn, Fe, Mn and Cr, considered to be partially adsorbed, particularly on silty and clayey particles, and co-precipitated on Fe and Mn oxyhydroxide forms precipitated in the topmost layers of sediments. Series of statistically significant relationships were established between trace metal concentrations and clay content and semi-quantitatively determined clay mineral species in the sediments.La reconstrucción paleoambiental de la Laguna de Aveiro se está realizando mediante la caracterización sedimentológica, paleoecológica, geoquímica y mineralógica de muestras de sedimento recogidas sistemáticamente en la misma. Este artículo presenta resultados relativos a las variaciones en la composición química y mineralógica de las fracciones fina (<63 μm) y arcillosa (<2 μm) de las muestras de sedimento de la Laguna de Aveiro, recogidas principalmente en las planicies intermareales bajas y depósitos submareales de los canales de Mira, Ílhavo y Ovar. Estos parámetros fueron utilizados para caracterizar los sedimentos de cada uno de los canales estudiados de la Laguna de Aveiro. Los sedimentos superficiales y subsuperficiales de esta laguna retienen cantidades relativamente elevadas de elementos vestigiales como Cu, Pb, Co, Ni, Cd, Zn, Fe, Mn y Cr, los cuales se consideran principalmente adsorbidos en partículas fangosas y arcillosas y en óxidos de Fe y Mn. Con base en los parámetros analizados se puede establecer una zonografía de la laguna. Se han encontrado relaciones entre las concentraciones de elementos vestigiales y el contenido de arcilla y las especies minerales de las arcillas en los sedimentos