1. S. AUBRY,The new concept of Transition by Breaking of Analyticity in a Crystallographic Modelin “Solitons and Condensed Matter Physics”, Solid State Sciences8(1978), pp. 264–277 (Springer) ed A.R. Bishop and T. Schneider.
2. I. PERCIVAL, J. Phys,A12(1979) L57.
3. C. RADIN,Low Temperature and the Origin of Crystalline Symmetry, Int. J. Mod. Phys.B1(1987), pp. 1157–1191 andDisordered Ground States of Classical Lattice Models Preprint(1990).
4. C. RADIN,Low Temperature and the Origin of Crystalline Symmetry, Int. J. Mod. Phys.B1(1987), pp. 1157–1191 andDisordered Ground States of Classical Lattice Models Preprint(1990).
5. For the Banach fixed point theorem see for example E. Zeidler “Nonlinear Functional Analysis and its Applications
l.Fixed-point Theorems” Theorem 1.A p. 17 and Proposition 1.2 p. 19. Springer (1986).