1,720,982 research outputs found
Twisted symmetries and integrable systems
No full textSymmetry properties are at the basis of integrability. In recent years, it appeared that so-called twisted symmetries are as effective as standard symmetries in many respects (integrating ODEs, finding special solutions to PDEs). Here we discuss how twisted symmetries can be used to detect integrability of Lagrangian systems which are not integrable via standard symmetries
Dynamical systems and σ-symmetries
No full textA deformation of the standard prolongation operation, defined on sets of vector fields in involution rather than on single ones, was recently introduced and christened ‘σ-prolongation’; correspondingly, one has ‘σ-symmetries’ of differential equations. These can be used to reduce the equations under study, but the general reduction procedure under σ-symmetries fails for equations of
order 1. In this paper, we discuss how σ-symmetries can be used to reduce
dynamical systems, i.e. sets of first-order ODEs in the form x'=f(x)
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
Noether theorem for mu-symmetries
No full textWe give a version of Noether theorem adapted to the framework of mu-symmetries; this extends to such case recent work by Muriel, Romero and Olver in the framework of lambda-symmetries, and connects mu-symmetries of a Lagrangian to a suitably modified conservation law. In some cases this 'mu-conservation law' actually reduces to a standard one; we also note a relation between mu-symmetries and conditional invariants. We also consider the case where the variational principle is itself formulated as requiring vanishing variation under mu-prolonged variation fields, leading to modified Euler-Lagrange equations. In this setting, mu-symmetries of the Lagrangian correspond to standard conservation laws as in the standard Noether theorem. We finally propose some applications and examples
Orbital Reducibility and a Generalization of Lambda Symmetries
No full textWe review the notion of reducibility and we introduce and discuss the notion of orbital reducibility for autonomous ordinary differential equations of first order. The relation between (orbital) reducibility and (orbital) symmetry is investigated and employed to construct (orbitally) reducible systems. By standard identifications, the notions extend to non-autonomous ODEs of first and higher order. Moreover we thus obtain a generalization of the lambda symmetries of Muriel and Romero. Several examples are given
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Side Conditions for Ordinary Differential Equations
No full textWe specialize Olver’s and Rosenau’s side condition heuristics for the determination of particular invariant sets of ordinary differential equations. It turns out that side conditions of so-called LaSalle type are of special interest. Moreover we put side condition properties of symmetric and partially symmetric
equations in a wider context. In the final section we present an application to parameter-dependent systems, in particular to quasi-steady state for chemical reactions
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