Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals
Search results

Search: All articles in the CMB digital archive with keyword resonance

 Expand all        Collapse all Results 1 - 4 of 4

1. CMB 2014 (vol 57 pp. 658)

Thang, Nguyen Tat
 Admissibility of Local Systems for some Classes of Line Arrangements Let $\mathcal{A}$ be a line arrangement in the complex projective plane $\mathbb{P}^2$ and let $M$ be its complement. A rank one local system $\mathcal{L}$ on $M$ is admissible if roughly speaking the cohomology groups $H^m(M,\mathcal{L})$ can be computed directly from the cohomology algebra $H^{*}(M,\mathbb{C})$. In this work, we give a sufficient condition for the admissibility of all rank one local systems on $M$. As a result, we obtain some properties of the characteristic variety $\mathcal{V}_1(M)$ and the Resonance variety $\mathcal{R}_1(M)$. Keywords:admissible local system, line arrangement, characteristic variety, multinet, resonance varietyCategories:14F99, 32S22, 52C35, 05A18, 05C40, 14H50

2. CMB 2010 (vol 54 pp. 56)

Dinh, Thi Anh Thu
 Characteristic Varieties for a Class of Line Arrangements Let $\mathcal{A}$ be a line arrangement in the complex projective plane $\mathbb{P}^2$, having the points of multiplicity $\geq 3$ situated on two lines in $\mathcal{A}$, say $H_0$ and $H_{\infty}$. Then we show that the non-local irreducible components of the first resonance variety $\mathcal{R}_1(\mathcal{A})$ are 2-dimensional and correspond to parallelograms $\mathcal{P}$ in $\mathbb{C}^2=\mathbb{P}^2 \setminus H_{\infty}$ whose sides are in $\mathcal{A}$ and for which $H_0$ is a diagonal. Keywords:local system, line arrangement, characteristic variety, resonance varietyCategories:14C21, 14F99, 32S22, 14E05, 14H50

3. CMB 2009 (vol 53 pp. 347)

Papageorgiou, Nikolaos S.; Staicu, Vasile
 Multiple Nontrivial Solutions for Doubly Resonant Periodic Problems We consider semilinear periodic problems with the right-hand side nonlinearity satisfying a double resonance condition between two successive eigenvalues. Using a combination of variational and degree theoretic methods, we prove the existence of at least two nontrivial solutions. Keywords:double resonance, generalized LL-condition, Leray-Schauder degree, Cerami conditionCategory:34B15

4. CMB 2001 (vol 44 pp. 323)

Schuman, Bertrand
 Une classe d'hamiltoniens polynomiaux isochrones Soit $H_0 = \frac{x^2+y^2}{2}$ un hamiltonien isochrone du plan $\Rset^2$. On met en \'evidence une classe d'hamiltoniens isochrones qui sont des perturbations polynomiales de $H_0$. On obtient alors une condition n\'ecessaire d'isochronisme, et un crit\ere de choix pour les hamiltoniens isochrones. On voit ce r\'esultat comme \'etant une g\'en\'eralisation du caract\ere isochrone des perturbations hamiltoniennes homog\`enes consid\'er\'ees dans [L], [P], [S]. Let $H_0 = \frac{x^2+y^2}{2}$ be an isochronous Hamiltonian of the plane $\Rset^2$. We obtain a necessary condition for a system to be isochronous. We can think of this result as a generalization of the isochronous behaviour of the homogeneous polynomial perturbation of the Hamiltonian $H_0$ considered in [L], [P], [S]. Keywords:Hamiltonian system, normal forms, resonance, linearizationCategories:34C20, 58F05, 58F22, 58F30
 top of page | contact us | privacy | site map |

© Canadian Mathematical Society, 2017 : https://cms.math.ca/