linear foliation
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2018 ◽  
Vol 11 (1) ◽  
pp. 189-196
Author(s):  
Kitha Mbitsa ◽  
Musa Ado Idris

This work is among the few studies conducted in Musawa sheet 56 NE, which is part of the basement complex rocks of TudunWulli - Kankia area. The study area lies between Latitude 12º 19ʹ 00ʹʹ to 12º 23ʹ 00ʹʹN and longitude 7º 42ʹ 00ʹʹ to 7º 46ʹ 00ʹʹN. Due to the continuous play of geologic processes on the earth, there is the need to continuously update the geology of the Nigeria basement complex as this has a very important economic implication especially in areas like mineral and groundwater exploration. Equally, less attention has been given to this sheet unlike other sheets within the zone. The study done in this area has revealed the various rock types and their geological characteristics: field relation, macroscopic and microscopic features as well as structural elements. Results from the study shows that the area consists of granite, migmatite- gneiss and quartzite which all display a variety of colors, textures and mineralogy. Careful analysis of the distinctive mineralogy, textures, optical and structural characteristics led to the nomenclature of the rocks. The migmatite-gneiss display two petrographic varieties base on their foliation: one with linear foliation of alternating light and dark color minerals, and the other with wave like foliation. While granite is generally fine to medium grained in texture. The dominant structural trend of joints and faults in the study area are NNE-SSW and NW-SE. All these trends are consistent with the general trends of the Nigeria basement rocks. A study of thin sections of the rocks under a petrological microscope reveals optical properties peculiar to each rock type. The type and nature of structural elements associated with the rocks together with their geometry reveal that the rocks have undergone more than one deformational event. The occurrence of numerous brittle and ductile structures shows that the area has a great potential for groundwater and mineralization. But the area still experience shortage of water for domestic purposes.Keywords: basement complex, brittle structures, foliation, petrographic varieties, thin sections


2010 ◽  
Vol 21 (04) ◽  
pp. 435-452 ◽  
Author(s):  
TOSHIKAZU ITO ◽  
BRUNO SCARDUA

We prove that a Morse type codimension one holomorphic foliation is not transverse to a sphere in the complex affine space. Also we characterize the variety of contacts of a linear foliation with concentric spheres.


1998 ◽  
Vol 08 (03) ◽  
pp. 483-503 ◽  
Author(s):  
Bernd Krauskopf ◽  
Hinke Osinga

We present an algorithm for computing the global two-dimensional unstable manifold of a hyperbolic fixed point or a normally hyperbolic invariant circle of a three-dimensional map. The global stable manifold can be obtained by considering the inverse map. Our algorithm computes intersections of the unstable manifold with a finite number of leaves of a chosen linear foliation. In this way, we obtain a growing piece of the unstable manifold represented by a mesh of prescribed quality. The performance of the algorithm is demonstrated with several examples.


1993 ◽  
Vol 13 (4) ◽  
pp. 697-704 ◽  
Author(s):  
Aziz El Kacimi Alaoui ◽  
Marcel Nicolau

AbstractWe consider foliations F obtained as the suspension of a linear foliation F0 on n by means of a linear Anosov diffeomorphism A of n keeping F0 invariant. Under suitable conditions on A the foliations F are shown to be C∞-stable, i.e. any differentiable foliation which is C∞-close to F is C∞-conjugated to F. The proof relies on a criterium of stability stated by R. Hamilton.


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