GRUP DE SISTEMES DINÀMICS UIB

Seminaris Fets (curs 2006/2007) :

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DIA: Dimecres 25 d'octubre
LLOC: Aula del Seminari GSD-UIB D-108
HORA: 15:30 -- 17:00
TITOL: A singular approach to Discontinuous Vector Fields
AUTOR: C. Buzzi, P. R. Da Silva i M. A. Teixeira
A CARREC DE: P. R. Da Silva
ABSTRACT: Singular perturbations problems in dimension three which are approximations of discontinuous vector fields are studied. The main result states that the regularization process developed by Sotomayor and Teixeira produces a singular problem for which the discontinuous set is a center manifold. Moreover, the definition of sliding vector field coincides with the reduced problem of the corresponding singular problem for a class of vector fields
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DIA: Divendres 27 d'octubre
LLOC: Aula del Seminari GSD-UIB D-108
HORA: 9:30 -- 11:00
TITOL: Limit cycles bifurcating from a k-dimensional isochronous center contained in $R^n$ with $k<=n$
AUTOR: J. Torregrosa (UAB) A CARREC DE: J. Torregrosa (UAB)
ABSTRACT:
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DIA: Divendres 17-nov-2006
LLOC: Seminari MatemÓtica Aplicada D-108
HORA: 9:30
TITOL: "Quadratic Perturbations of a Class of Quadratic Reversible systems with two centers."
AUTORS: B. Coll (UIB), Chengzhi Li (Peking University).i R. Prohens (UIB)
A CARREC DE: Rafel Prohens
ABSTRAC: The weak Hilbert 16th problem was solved completely in the quadratic case; that is, the least upper bound of the number of zeros of the Abelian integrals associated with quadratic perturbations of quadratic Hamiltonian systems is known.
The next natural step is to consider the same problem for quadratic integrable but non-Hamiltonian systems. Most mathematicians working in this field believe that perturbations of the quadratic reversible systems, especially with two centers, may give the richest dynamical behavior.
In this work we consider quadratic perturbations of a one-parameter family of quadratic reversible non-Hamiltonian systems, with two centers and without other singularities in the finite plane. For such family, we give an upper bound of the limit cycles that emerge from each of the two period annuli and we prove that it is sharp. Even more, we present the exact configuration of limit cycles that can be and the corresponding bifurcation diagrams.
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DIA: Divendres 1-desembre-2006
LLOC: Seminari MatemÓtica Aplicada D-108
HORA: 9:30
TITOL: "Quadratic Perturbations of a Class of Quadratic Reversible systems with two centers. Part II"
AUTORS: B. Coll (UIB), Chengzhi Li (Peking University).i R. Prohens (UIB)
A CARREC DE: Tomeu Coll
ABSTRAC: The weak Hilbert 16th problem was solved completely in the quadratic case; that is, the least upper bound of the number of zeros of the Abelian integrals associated with quadratic perturbations of quadratic Hamiltonian systems is known. The next natural step is to consider the same problem for quadratic integrable but non-Hamiltonian systems. Most mathematicians working in this field believe that perturbations of the quadratic reversible systems, especially with two centers, may give the richest dynamical behavior. In this work we consider quadratic perturbations of a one-parameter family of quadratic reversible non-Hamiltonian systems, with two centers and without other singularities in the finite plane. For such family, we give an upper bound of the limit cycles that emerge from each of the two period annuli and we prove that it is sharp. Even more, we present the exact configuration of limit cycles that can be and the corresponding bifurcation diagrams.
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DIA: Divendres 19-gener-2007
LLOC: Seminari MatemÓtica Aplicada D-108
HORA: 9:30
TITOL: "El problema de demosaicing"
AUTORS: Toni Buades (UIB) i Catalina Sbert (UIB)
A CARREC DE: Catalina Sbert (UIB)
ABSTRAC: Definirem el problema de demosaicing i farem una revisiˇ dels algorismes existents mŔs importants amb els problemes que presenten. Proposarem un nou mŔtode basat en el NL-means que millora els resultats existents fins ara. ***********************************************************************
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DIA: Divendres 26-gener-2007
LLOC: Seminari MatemÓtica Aplicada D-108
HORA: 9:30
TITOL: "Abel--like equations with no periodic solutions"
AUTORS: Joan Torregrosa Ar˙s (UAB)
A CARREC DE: Joan Torregrosa Ar˙s (UAB)
ABSTRAC: In this paper, we show several criteria for the non-exitence of positive periodic solutions on generalized Abel equations with periodic coefficients. As an application, some families of planar vector fields without limit cycles are obtained. ***********************************************************************
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DIA: Divendres 23-marš-2007
LLOC: Seminari MatemÓtica Aplicada D-108
HORA: 9:30
TITOL: "Joint decompression of a satellite stereo pair of images"
AUTORS: Toni Buades Capˇ (UIB)
A CARREC DE: Toni Buades Capˇ (UIB)
ABSTRAC: In order to reconstruct a digital elevation model of the terrain, satellite images are taken by pairs with a small time delay. To take into account the transmission limitations only one image of the pair is compressed . The compressed image must be restored digitally once it has been received. Algorithms in the literature are applied only to a single image and they are not able to take advantage of the information of the non compressed image. The objective of this talk is to show the feasibility of a joint decompression algorithm of a stereo pair. The key idea is to transfer information from the non compressed image to restore the compressed one. The proposed algorithm is based on the recently introduced algorithm NL-means. This algorithm is used to detect similarities and self similarities between the two images and then it transports the information lost from the non compressed image to the compressed one. ***********************************************************************
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DIA: Divendres 30-marš-2007
LLOC: Seminari MatemÓtica Aplicada D-108
HORA: 9:30
TITOL: "Some extensions of the PoincarÚ compactification"
AUTORS: Jaume Llibre (UAB) i Antonio E. Teruel (UIB)
A CARREC DE: Antonio E. Teruel (UIB)
ABSTRAC: The PoincarÚ Compactification is a technique to extent polynomial vector fields to a compact manifold. In this talk we will explain different extensions of this technique to a nonpolynomial vector fields and we will pay attention to the necessary conditions for a function to be compactificable. ***********************************************************************
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DIA: Divendres 04-Abril-2007
LLOC: Seminari MatemÓtica Aplicada D-108
HORA: 9:30
TITOL: "On the critical remarkable values of the rational first integrals of polynomial vector fields"
AUTORS: Jaume Llibre (UAB) i Antoni Ferragut (UAB)
A CARREC DE: Antoni Ferragut (UAB)
ABSTRAC: Some properties which relate the inverse integrating factor and the remarkable values of a rational (or polynomial) first integral are presented. It is also showed the importance of the curves $f+cg=0$ when $c$ is a remarkable value and $H=f/g$ is a rational first integral. ***********************************************************************
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DIA: Divendres 20-Abril-2007
LLOC: Seminari MatemÓtica Aplicada D-108
HORA: 9:30
TITOL: "Watermarking frÓgil i morfologia matemÓtica"
AUTORS: JosÚ Luis Lisani (UIB)
A CARREC DE: JosÚ Luis Lisani (UIB)
ABSTRAC: Un watermark Ús una modificaciˇ controlada d'una imatge, imperceptible per l'ull humÓ per˛ detectable amb mŔtodes algoritmics. Un watermark frÓgil tÚ la propietat d'esdevenir indetectable quan la imatge que el contÚ pateix alguna modificaciˇ, per petita que sigui. Per aquest motiu els watermarks frÓgils s'utilitzen per verificar l'autenticitat d'una imatge. En aquesta xerrada es donarÓ una visiˇ general del problema del watermarking, es descriuran algunes de les tŔcniques habituals per insertar i detectar watermarks en imatges digitals i es discutirÓ la possibilitat d'aplicar conceptes i tŔcniques de la morfol˛gia matemÓtica al watermarking frÓgil. ***********************************************************************
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DIA: Divendres 04-Maig-2007
LLOC: Seminari MatemÓtica Aplicada D-108
HORA: 9:30
TITOL: "Ďrbites peri˛diques per equacions diferencials no aut˛nomes"
AUTORS: Tomeu Coll (UIB) i Rafel Prohens (UIB)
A CARREC DE: Tomeu Coll (UIB)
ABSTRAC: ***********************************************************************
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