منابع مشابه
Formation of singularities for equivariant 2+1 dimensional wave maps into the two-sphere
In this paper we report on numerical studies of the Cauchy problem for equivariant wave maps from 2+1 dimensional Minkowski spacetime into the two-sphere. Our results provide strong evidence for the conjecture that large energy initial data develop singularities in finite time and that singularity formation has the universal form of adiabatic shrinking of the degree-one harmonic map from R into S.
متن کاملA Computing all maps into a sphere
Given topological spaces X,Y , a fundamental problem of algebraic topology is understanding the structure of all continuous maps X → Y . We consider a computational version, where X,Y are given as finite simplicial complexes, and the goal is to compute [X,Y ], i.e., all homotopy classes of such maps. We solve this problem in the stable range, where for some d ≥ 2, we have dimX ≤ 2d−2 and Y is (...
متن کاملFormation of singularities for equivariant 2+1 dimensional wave maps into two-sphere
In this paper we report on numerical studies of the Cauchy problem for equivariant wave maps from 2+1 dimensional Minkowski spacetime into the two-sphere. Our results provide strong evidence for the conjecture that large energy initial data develop singularities in finite time and that singularity formation has the universal form of adiabatic shrinking of the degree-one harmonic map from R into S.
متن کاملEquivariant self-similar wave maps from Minkowski spacetime into 3-sphere
We prove existence of a countable family of spherically symmetric self-similar wave maps from the Minkowski spacetime into the 3-sphere. These maps can be viewed as excitations of the ground state wave map found previously by Shatah. The first excitation is particularly interesting in the context of the Cauchy problem since it plays the role of a critical solution sitting at the threshold of si...
متن کاملLocally Stable Maps of the 3-Sphere into 4-Space
We classify locally stable maps from the 3-sphere to 4-space up to homotopy through locally stable maps. The equivalence class of a locally stable map f is determined by the isotopy type τ(f) of its framed singularity link, its generalized normal degree ν(f), and the algebraic number of cusps κ(f) of any generic extension of f to a map of the 4-disk into 5-space. Furthermore, relations between ...
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ژورنال
عنوان ژورنال: Revista De La Union Matematica Argentina
سال: 2022
ISSN: ['0041-6932', '1669-9637']
DOI: https://doi.org/10.33044/revuma.3159