An Isotopic Perturbation Lemma Along Periodic Orbits

A well-known lemma by John Franks asserts that one obtains any perturbation of the derivative of a diffeomorphism along a periodic orbit by a $C^1$-perturbation of the whole diffeomorphism on a small neighbourhood of the orbit. However, one does not control where the invariant manifolds of the orbit are, after perturbation. We show that if the perturbated derivative is obtained by an isotopy along which some strong stable/unstable manifolds of some dimensions exist, then the Franks perturbation can be done preserving the corresponding stable/unstable semi-local manifolds. This is a general perturbative tool in $C^1$-dynamics that has many consequences. We give simple examples of such consequences, for instance a generic dichotomy between dominated splitting and small stable/unstable angles inside homoclinic classes.Comment: 51 pages. arXiv admin note: substantial text overlap with arXiv:0912.112

OMA-DD : outils de médiation et d'apprentissage au service du développement durable

rapport finalL'ingénierie écologique se plaçant dans une perspective globale de gestion durable fondée sur la prise en compte des interactions entre nature et sociétés, l'objectif de cette proposition est 1) de poursuivre une réflexion interdisciplinaire et finalisée engagée sur les interactions entre dynamiques naturelles et dynamiques sociales dans un territoire en mutation d'intérêt patrimonial (l'île d'Ouessant, réserve de biosphère) qui a conduit à l'élaboration d'un modèle conceptuel et d'un prototype informatique ; 2) d'adapter ces productions de la recherche à deux contextes opérationnels différents (gestion, éducation) de manière à permettre leur appropriation par la société civile en tant qu'outils de gestion, de médiation et d'apprentissage ; 3) de porter un regard critique sur l'utilisation participative de ces outils hérités des technologies de l'information géographique par différents types d'acteur dans des contextes de gestion intégrée et de développement durable

OMA-DD : outils de médiation et d'apprentissage au service du développement durable

rapport finalL'ingénierie écologique se plaçant dans une perspective globale de gestion durable fondée sur la prise en compte des interactions entre nature et sociétés, l'objectif de cette proposition est 1) de poursuivre une réflexion interdisciplinaire et finalisée engagée sur les interactions entre dynamiques naturelles et dynamiques sociales dans un territoire en mutation d'intérêt patrimonial (l'île d'Ouessant, réserve de biosphère) qui a conduit à l'élaboration d'un modèle conceptuel et d'un prototype informatique ; 2) d'adapter ces productions de la recherche à deux contextes opérationnels différents (gestion, éducation) de manière à permettre leur appropriation par la société civile en tant qu'outils de gestion, de médiation et d'apprentissage ; 3) de porter un regard critique sur l'utilisation participative de ces outils hérités des technologies de l'information géographique par différents types d'acteur dans des contextes de gestion intégrée et de développement durable

La géoprospective – Apport de la dimension spatiale aux démarches prospectives

International audienceAssimilée à une forme particulière de prospective, la géoprospective est née de la convergence entre géographie, modélisation et prospective. Son objectif consiste à mieux intégrer, à l'aide de diverses méthodes, le territoire dans le processus d'exploration du futur, allant au-delà d'une simple fonction de support illustratif de ses devenirs possibles. Trois champs de recherche ont contribué à son développement : la modélisation d'accompagnement, la prospective et lamodélisation des changements d'occupation et d'utilisation des sols. Cet article présente un rapide état de l'art de la géoprospective et introduit quelques recommandations quant à l'usage des modèles qui la sous-tendent

Role-Playing Game and Learning for Young People About Sustainable Development Stakes: An Experiment in Transferring and Adapting Interdisciplinary Scientific Knowledge

The study refers to the interactions between socio-economic and natural dynamics in an island biosphere reserve by using companion modelling. This approach provides scientific results and involves interdisciplinarity. In the second phase of the study, we transferred knowledge by adapting the main research output, a role-playing game, to young people. Our goal was to introduce interactions between social and ecological systems, coastal dynamics and integrated management. Adapting the game required close collaboration between the scientists and educators in order to transform both its substance and form and to run it with an easy-to-handle ergonomic platform.Children Education, Multi-Agent Environment, Role-Playing Game

Cantor Spectrum for Schr\"odinger Operators with Potentials arising from Generalized Skew-shifts

We consider continuous $SL(2,\mathbb{R})$-cocycles over a strictly ergodic homeomorphism which fibers over an almost periodic dynamical system (generalized skew-shifts). We prove that any cocycle which is not uniformly hyperbolic can be approximated by one which is conjugate to an $SO(2,\mathbb{R})$-cocycle. Using this, we show that if a cocycle's homotopy class does not display a certain obstruction to uniform hyperbolicity, then it can be $C^0$-perturbed to become uniformly hyperbolic. For cocycles arising from Schr\"odinger operators, the obstruction vanishes and we conclude that uniform hyperbolicity is dense, which implies that for a generic continuous potential, the spectrum of the corresponding Schr\"odinger operator is a Cantor set.Comment: Final version. To appear in Duke Mathematical Journa

GIS spatio-temporal modeling of human maritime activities

4 pages, session "Marine Spatial Planning and Human Impacts"International audienceCoastal seas are important for human societies with many and diverse activities. These space and resource consuming activities exert an increasing pressure on the environment and sometimes result in conflicting interactions. Understanding these interactions remains a challenge for research and civil society. A methodology is proposed to describe the spatio-temporal distribution of several activities in coastal seas. An application is developed in the Bay of Brest (Brittany, France). Spatial, temporal, quantitative and qualitative data acquisition combines analysis of spatio-temporal databases and results from interviews. The heterogeneous data collected are stored in a spatiotemporal database (STDB). Firstly, the STDB is used with a GIS to produce temporal snapshots of daily human activity patterns over a one-year period. Secondly, using the STBD we can identify, quantify and map potential uses conflicts in space and time between activities in the Bay of Brest

Universal regular control for generic semilinear systems

We consider discrete-time projective semilinear control systems $\xi_{t+1} = A(u_t) \cdot \xi_t$, where the states $\xi_t$ are in projective space $\mathbb{R}P^{d-1}$, inputs $u_t$ are in a manifold $U$ of arbitrary finite dimension, and $A \colon U \to GL(d,\mathbb{R})$ is a differentiable mapping. An input sequence $(u_0,\ldots,u_{N-1})$ is called universally regular if for any initial state $\xi_0 \in \mathbb{R}P^{d-1}$, the derivative of the time-$N$ state with respect to the inputs is onto. In this paper we deal with the universal regularity of constant input sequences $(u_0, \dots, u_0)$. Our main result states that generically in the space of such systems, for sufficiently large $N$, all constant inputs of length $N$ are universally regular, with the exception of a discrete set. More precisely, the conclusion holds for a $C^2$-open and $C^\infty$-dense set of maps $A$, and $N$ only depends on $d$ and on the dimension of $U$. We also show that the inputs on that discrete set are nearly universally regular; indeed there is a unique non-regular initial state, and its corank is $1$. In order to establish the result, we study the spaces of bilinear control systems. We show that the codimension of the set of systems for which the zero input is not universally regular coincides with the dimension of the control space. The proof is based on careful matrix analysis and some elementary algebraic geometry. Then the main result follows by applying standard transversality theorems.Comment: 48 pages. This version incorporates suggestions and corrections by the referees. It also includes arXiv:1201.2217 as an Appendi