1,031 research outputs found
A two-parameter control for contractive-like multivalued mappings
We propose a general approach to defining a contractive-like multivalued
mappings which avoids any use of the Hausdorff distance between the sets
and . Various fixed point theorems are proved under a
two-parameter control of the distance function between
a point and the value F(x) \ss X. Here, both parameters are
numerical functions. The first one \a\,:[0,+\i)\rightarrow [1,+\i) controls
the distance between and some appropriate point in comparison
with , whereas the second one \b\,:[0,+\i)\rightarrow [0,1)
estimates with respect to . It appears that the well
harmonized relations between \a and \b are sufficient for the existence of
fixed points of . Our results generalize several known fixed-point theorems
Relation-based Galois connections: towards the residual of a relation
Inma P. Cabrera, Pablo Cordero, Manuel Ojeda-Aciego, Relation-based Galois connections: towards the residual of a relation, CMMSE 2017: Proceedings of the 17th International Conference on Mathematical Methods in Science and Engineering ( ISBN: 978-84-617-8694-7) , pp. 469--475We explore a suitable generalization of the notion of Galois connection in which their components are binary relations. Many different approaches are possible depending both on the (pre-)order relation between subsets in the underlying powerdomain and the chosen type of relational composition.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech
Large Dual Transformations and the Petrov-Diakonov Representation of the Wilson Loop
In this work, based on the Petrov-Diakonov representation of the Wilson loop
average W in the SU(2) Yang-Mills theory, together with the Cho-Fadeev-Niemi
decomposition, we present a natural framework to discuss possible ideas
underlying confinement and ensembles of defects in the continuum. In this
language we show how for different ensembles the surface appearing in the
Wess-Zumino term in W can be either decoupled or turned into a variable, to be
summed together with gauge fields, defects and dual fields. This is discussed
in terms of the regularity properties imposed by the ensembles on the dual
fields, thus precluding or enabling the possibility of performing the large
dual transformations that would be necessary to decouple the initial surface.Comment: 35 pages, LaTeX, corrected version, accepted for publication in Phys.
Rev.
The Forced van der Pol Equation II: Canards in the reduced system
This is the second in a series of papers about the dynamics of the forced van der Pol oscillator [J. Guckenheimer, K. Hoffman, and W. Weckesser, SIAM J. Appl. Dyn. Syst., 2 (2003), pp. 1–35].
The first paper described the reduced system, a two dimensional flow with jumps that reflect fast trajectory segments in this vector field with two time scales. This paper extends the reduced system to account for canards, trajectory segments that follow the unstable portion of the slow manifold in the forced van der Pol oscillator. This extension of the reduced system serves as a template for approximating the full nonwandering set of the forced van der Pol oscillator for large sets of parameter values, including parameters for which the system is chaotic. We analyze some bifurcations in the extension of the reduced system, building upon our previous work in [J. Guckenheimer, K. Hoffman, and W. Weckesser, SIAM J. Appl. Dyn. Syst., 2 (2003), pp. 1–35]. We conclude with computations of return maps and periodic orbits in the full three dimensional flow that are compared with the computations and analysis of the reduced system. These comparisons demonstrate numerically the validity of results we derive from the study of canards in the reduced system
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