Results 1 to 10 of about 244,947 (267)
On singularity confinement for the pentagram map [PDF]
Journal of Algebraic Combinatorics, 2012 The pentagram map, introduced by R. Schwartz, is a birational map on the configuration space of polygons in the projective plane. We study the singularities of the iterates of the pentagram map.
Max Glick
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Singularity confinement as an integrability criterion [PDF]
Journal of Physics A: Mathematical and Theoretical, 2019 Abstract In this paper we present a rigorous method for deciding whether a birational three point mapping that has the singularity confinement property is integrable or not, based only on the structure of its (confined) singularity patterns.
Basile Grammaticos +2 more
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Bridging the chiral symmetry and confinement with singularity
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 2020 We consider a holographic quark model where the confinement is a consequence of the quark condensate. Surprisingly, the equation of motion of our holographic model can be mapped to the old spin-less bag model.
Sang-Jin Sin
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Full-deautonomisation of a class of second-order mappings in ancillary form [PDF]
Open Communications in Nonlinear Mathematical Physics, 2023 We present an application of the full-deautonomisation method to a class of secondorder mappings which, using an ancillary variable, can be cast into a form that greatly facilitates the study of their singularities.
Basil Grammaticos, Ralph Willox
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Bilinearization of discrete soliton equations and singularity confinement [PDF]
Physics Letters, Section A: General, Atomic and Solid State Physics, 1997 14 pages ...
Masayuki Oikawa, Kenichi Maruno
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SIGMA-MESON AND CONFINEMENT SINGULARITY [PDF]
Gribov-80 Memorial Volume, 2011 ) into twopoles which are diving on the second sheet of the complex-s plane. Thepoles correspond to states which are mixtures of gluonic, flavour-singlet qq¯,and ππ components. The low-lying pole is located at the complex-M region(690 ± 160) − i(400 ± 150) MeV, the second one goes in the region of largemasses: (ReM >∼ 1400, −ImM >∼ 500) MeV.
V A Nikonov, V V Anisovich
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Singularity Confinement and Chaos in Discrete Systems [PDF]
Physical Review Letters, 1998 We present a number of second order maps, which pass the singularity confinement test commonly used to identify integrable discrete systems, but which nevertheless are non-integrable. As a more sensitive integrability test, we propose the analysis of the complexity (``algebraic entropy'') of the map using the growth of the degree of its iterates ...
Jarmo Hietarinta
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Point singularity array with metasurfaces [PDF]
Nature Communications, 2023 Phase singularities are loci of darkness surrounded by monochromatic light in a scalar field, with applications in optical trapping, super-resolution imaging, and structured light-matter interactions.
Soon Wei Daniel Lim +6 more
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Singularity confinement in delay-differential Painlevé equations
Journal of Physics A: Mathematical and Theoretical, 2020 Abstract We study singularity confinement phenomena in examples of delay-differential Painlevé equations, which involve shifts and derivatives with respect to a single independent variable. We propose a geometric interpretation of our results in terms of mappings between jet spaces, defining certain singularities analogous to those of ...
Alexander Stokes
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Singularity confinement and algebraic entropy: the case of the discrete Painlevé equations [PDF]
Physics Letters, Section A: General, Atomic and Solid State Physics, 1999 We examine the validity of the results obtained with the singularity confinement integrability criterion in the case of discrete Painlevé equations. The method used is based on the requirement of non-exponential growth of the homogeneous degree of the iterate of the mapping.
Basile Grammaticos, K M Tamizhmani
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