323,009 research outputs found
"Symmetry and Perturbation Theory'', Proceedings of the International Conference SPT2004
No full textThis proceedings volume is a collection of papers presented at the International Conference on SPT2004 focusing on symmetry, perturbation theory, and integrability.
The book provides an updated overview of the recent developments in the various different fields of nonlinear dynamics, covering both theory and applications. Special emphasis is given to algebraic and geometric integrability, solutions to the N-body problem of the “choreography” type, geometry and symmetry of dynamical systems, integrable evolution equations, various different perturbation theories, and bifurcation analysis.
The contributors to this volume include some of the leading scientists in the field, among them: I Anderson, D Bambusi, S Benenti, S Bolotin, M Fels, W Y Hsiang, V Matveev, A V Mikhailov, P J Olver, G Pucacco, G Sartori, M A Teixeira, S Terracini, F Verhulst and I Yehorchenko
Terracini loci of curves
No full textWe study subsets S of curves X whose double structure does not impose independent conditions to a linear series L, but there are divisors D∈ | L| singular at all points of S. These subsets form the Terracini loci of X. We investigate Terracini loci, with a special look towards their non-emptiness, mainly in the case of canonical curves, and in the case of space curves
SPT 2004 - Symmetry and Perturbation Theory
No full textSPT 2004
Symmetry and Perturbation Theory
30 May - 6 June 2004, Cala Gonone (Sardinia, Italy)
Scientific Committee:
S. Abenda (Bologna, I), D. Bambusi (Milano, I), G. Cicogna (Pisa, I),
A. Degasperis (Roma, I), G. Gaeta (Milano, I), V. Kuznetsov (Leeds, UK),
G. Marmo (Napoli, I), P. Olver (Minneapolis, USA), J.P. Ortega (Besançon, F),
S. Rauch (Linkoping, S), E. Sousa Dias (Lisboa, P), S. Terracini (Milano, I),
F. Verhulst (Utrecht, NL), S. Walcher (Aachen, D), B. Zhilinskii (Dunquerque, F)
Organizing Commitee:
A. Degasperis (Roma), G. Gaeta (Milano), B. Prinari (Lecce), S. Terracini (Milano)
The conference is the fifth of a series begun in 1996. The principal aim of the series of conference is to join together researchers from areas of pure and applied mathematics, physics and chemistry to present their most recent and innovative achievements in the field of symmetries, perturbation and integrable systems.
Conference proceedings are published by World Scientific
On the Terracini locus of projective varieties
No full textWe introduce and study properties of the Terracini locus of projective varieties X, which is the locus
of finite subsets S such that 2S fails to impose independent conditions to a linear system L. Terracini loci
are relevant in the study of interpolation problems over double points in special position, but they also enter naturally
in the study of special loci contained in secant varieties to projective varieties.
We find some criteria which exclude that a set S belongs to the Terracini locus. Furthermore, in the case
where X is a Veronese variety, we bound the dimension of the Terracini locus and we determine examples
in which the locus has codimension 1 in the symmetric product of X
The nodal set of solutions to some elliptic problems: Singular nonlinearities
No full textThis paper deals with solutions to the equation-Delta u = lambda(+ )(u(+))(q-1) - lambda(-)(u(-))(q-1 )in B-1where lambda(+), lambda(-) > 0, q is an element of (0, 1), B-1 = B-1(0) is the unit ball in R-N, N >= 2, and u(+) := maxu, 0, u(-) := max-u, 0 are the positive and the negative part of u, respectively. We extend to this class of singular equations the results recently obtained in [25] for sublinear and discontinuous equations, 1 <= q < 2, namely: (a) the finiteness of the vanishing order at every point and the complete characterization of the order spectrum; (b) a weak non-degeneracy property; (c) regularity of the nodal set of any solution: the nodal set is a locally finite collection of regular codimension one manifolds up to a residual singular set having Hausdorff dimension at most N - 2 (locally finite when N = 2). As an intermediate step, we establish the regularity of a class of not necessarily minimal solutions.The proofs are based on a priori bounds, monotonicity formulae for a 2-parameter family of Weiss-type functionals, blow-up arguments, and the classification of homogeneous solutions. (C) 2019 Elsevier Masson SAS. All rights reserved
Subharmonic solutions to second order differential equations with periodic nonlinearities
No full textA Note on the Complete Rotational Invariance of Biradial Solutions to Semilinear Elliptic Equations
No full textWe investigate symmetry properties of solutions to equations of the form -Δu =a/|x|2u + f (|x|,u) in R for N ≥ 4, with at most critical nonlinearities. By using geometric arguments, we prove that solutions with low Morse index (namely 0 or 1) and which are biradial (i.e. are invariant under the action of a toric group of rotations), are in fact completely radial. A similar result holds for the semilinear Laplace-Beltrami equations on the sphere. Furthermore, we show that the condition on the Morse index is sharp. Finally we apply the result in order to estimate best constants of Sobolev type inequalities with different symmetry constraints
On the existence of homoclinic solutions for almost periodic second order systems
No full textIn this paper we prove the existence of at least one homoclinic solution for a second order Lagrangian system, where the potential is an almost periodic function of time. This result generalizes existence theorems known to hold when the dependence on time of the potential is periodic. The method is of a variational nature, solutions being found as critical points of a suitable functional. The absence of a group of symmetries for which the functional is invariant (as in the case of periodic potentials) is replaced by the study of problems ''at infinity'' and a suitable use of a property introduced by E. Sere
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