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# Documents  Yi, Yingfei | enregistrements trouvés : 5

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## Post-edited  Perturbative techniques of the dynamics in the $C^1$-topology Crovisier, Sylvain (Auteur de la Conférence) | CIRM (Editeur )

These lectures will address the dynamics of vector fields or diffeomorphisms of compact manifolds. For the study of generic properties or for the construction of examples, it is often useful to be able to perturb a system. This generally leads to delicate problems: a local modification of the dynamics may cause a radical change in the behavior of the orbits. For the $C^1$-topology, various techniques have been developed which allow to perturb while controlling the dynamics: closing and connection of orbits, perturbation of the tangent dynamics... We derive various applications to the description of $C^1$-generic diffeomorphisms. These lectures will address the dynamics of vector fields or diffeomorphisms of compact manifolds. For the study of generic properties or for the construction of examples, it is often useful to be able to perturb a system. This generally leads to delicate problems: a local modification of the dynamics may cause a radical change in the behavior of the orbits. For the $C^1$-topology, various techniques have been developed which allow to perturb ...

## Multi angle  Dynamics of bounded solutions of parabolic equations on the real line - Part 1 Polacik, Peter (Auteur de la Conférence) | CIRM (Editeur )

We consider parabolic equations of the form $u_t = u_{xx} + f (u)$ on the real line. Unlike their counterparts on bounded intervals, these equations admit bounded solutions whose large-time dynamics is not governed by steady states. Even with respect to the locally uniform convergence, the solutions may not be quasiconvergent, that is, their omega-limit sets may contain nonstationary solutions.
We will start this lecture series by exhibiting several examples of non-quasiconvergent solutions, discussing also some entire solutions appearing in their omega-limit sets. Minimal assumptions on the nonlinearity are needed in the examples, which shows that non-quasiconvergent solutions occur very frequently in this type of equations. Our next goal will be to identify specific classes of initial data that lead to quasiconvergent solutions. These include localized initial data (joint work with Hiroshi Matano) and front-like initial data. Finally, in the last part of these lectures, we take a more global look at the solutions with such initial data. Employing propagating terraces, or stacked families of traveling fronts, we describe their entire spatial profile at large times.
We consider parabolic equations of the form $u_t = u_{xx} + f (u)$ on the real line. Unlike their counterparts on bounded intervals, these equations admit bounded solutions whose large-time dynamics is not governed by steady states. Even with respect to the locally uniform convergence, the solutions may not be quasiconvergent, that is, their omega-limit sets may contain nonstationary solutions.
We will start this lecture series by exhibiting ...

## Multi angle  Dissipativity in nonautonomous linear-quadratic control processes Núñez, Carmen (Auteur de la Conférence) | CIRM (Editeur )

This talk concerns the concept of dissipativity in the sense of Willems for nonautonomous linear-quadratic (LQ) control systems. A nonautonomous system of Hamiltonian ODEs can be associated with such an LQ system, and the analysis of the corresponding symplectic dynamics provides valuable information on the dissipativity properties. The presence of exponential dichotomy, the occurrence of weak disconjugacy, and the existence of nonnegative solutions of the Riccati equation provided by the Hamiltonian system are closely related to the presence of (normal or strict) dissipativity and to the definition of the (normal or strong) storage functions.
This is a joint work with: Roberta Fabbri, Russell Johnson, Sylvia Novo and Rafael Obaya.
This talk concerns the concept of dissipativity in the sense of Willems for nonautonomous linear-quadratic (LQ) control systems. A nonautonomous system of Hamiltonian ODEs can be associated with such an LQ system, and the analysis of the corresponding symplectic dynamics provides valuable information on the dissipativity properties. The presence of exponential dichotomy, the occurrence of weak disconjugacy, and the existence of nonnegative ...

## Multi angle  Dichotomy, the closed range theorem and optimal control Brunovsky, Pavel (Auteur de la Conférence) | CIRM (Editeur )

Necessary conditions for infinite horizon optimal controls problem can be obtained by the alternative theorem. This theorem requires that the range of a shift operator on a functional space is closed. It will be shown that this is the case if the dynamics of the problem is hyperbolic but may fail to be so if it is not.

## Multi angle  Geometric control and dynamics Rifford, Ludovic (Auteur de la Conférence) | CIRM (Editeur )

The geometric control theory is concerned with the study of control systems in finite dimension, that is dynamical systems on which one can act by a control. After a brief introduction to controllability properties of control systems, we will see how basic techniques from control theory can be used to obtain for example generic properties in Hamiltonians dynamics.

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