- Éditeur: Coédition CNRS/EDP Sciences
- ISBN: 978-2-7598-1738-2
- Pages: 262
**Publié:**04/12/2015**Note:**5/5 |*163 votes sur Amazon.fr*

Group Action analysis developed and applied mainly by Louis Michel to the study of N-dimensional periodic lattices is the central subject of the book. Different basic mathematical tools currently used for the description of lattice geometry are introduced and illustrated applications through to crystal Structures in two- and three-dimensional space, to abstract multi-dimensional lattices and to lattices associated with integrable dynamical systems. Starting from general Delone sets the authors turn to different symmetry and explicit topological classifications including construction of orbifolds for two- and three-dimensional point and Space groups. Voronoï Delone and cells together with positive quadratic forms and lattice description by root systems are introduced to demonstrate alternative approaches to lattice geometry study. Zonohedral Zonotopes and families of 2,- 3,- 4,- 5-dimensional lattices are explicitly visualized using graph theory approach. Along with applications crystallographic qualitative features of lattices of quantum states appearing for quantum problems associated with classical integrable Hamiltonian dynamical systems are discussed shortly. The presentation of the material is presented through a number of concrete examples with an extensive use of graphical visualization. The book is aimed at graduated and post graduate students and young researchers in theoretical physics, dynamical systems, applied mathematics, Solid state physics, crystallography, molecular physics, Theoretical chemistry,…

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