GRADIENT PATTERN ANALYSIS OF TOPOLOGICAL
DEFORMATIONS IN DYNAMICAL MANIFOLDS
Cristiane P. Camilo, Reinaldo R. Rosa, N. Vijaykumar,
Fernando M. Ramos(1)
and Marcelo
Rebouças(2)
(1) INPE
(2) CBPF
Characterization of local
response due to topological deformation in extended dynamical manifolds is a
key problem to understand the role of geometrical singularities to the global
stability of the manifold during its spatio-temporal evolution. Here, we
present a 2D single extended dynamical manifold based on the Laplacian of a
scalar function on a triangulated surface. This surface is divided in two
regions: (a) where a local deformation occurs and (b) where the effect of this
deformation reaches. The application of the Gradient Pattern Analysis on these
regions under different deformations shows that the topological deformation is
undetectable if the local asymmetry is Less than a critical value depending on
the manifold extension. We also discuss the deformation detectability in
hyperbolic manifolds and its application for direct recognition of multiple
images in cosmological topologies.