Index
0 Introduction
1 Extended states
1.1 Homogeneous states and their stability
1.2 Stability of homogeneous states in one-way CML
1.3 Stability of homogeneous states in diffusive CML
1.4 Stability of periodic global states
2 Localized states and propagating fronts
2.1 Localized states
2.2 Travelling velocity and basic properties
3 Travelling waves
3.1 A bistable local map f
3.2 Travelling waves in one-way CML
3.3 Travelling waves in diffusive CML
3.4 Mode-locking of the travelling velocity
4 A piece-wise linear local map
4.1 The piece-wise linear local map
4.2 The auxiliary map and its symbolic dynamics
4.2.1 The auxiliary map for an increasing step state
4.2.2 The auxiliary map for a decreasing step state
4.2.3 Symbolic dynamics of minimal 1-states
4.3 The travelling velocity
4.3.1 Existence of the travelling velocity
4.3.2 Continuity of the travelling velocity
4.3.3 The travelling velocity is non-decreasing
4.3.4 The velocity tree
4.4 Mode-locking of the auxiliary map
4.4.1 Mode-locking
4.4.2 Stability diagram of the auxiliary map
4.4.3 Velocity in the zero-gap case
4.5 Representing the velocity tree with an integral lattice
4.5.1 The integral lattice
4.5.2 Concatenating sequences using the lattice representation
4.5.3 Concatenating a family of sequences
4.5.4 Unimodular transformations and envelopes
5 Higher order interface dynamics
5.1 High order dynamics of minimal states
5.1.1 Convergence to minimal states
5.1.2 Two-dimensional auxiliary map
5.1.3 The tongues for the two-dimensional case
5.1.4 Higher order dynamics
5.2 Mode-locking for smooth maps
5.2.1 Mode-locking in one-way CMLs
5.2.2 Mode-locking in diffusive CMLs
5.3 Width of the mode-locking plateaus
5.3.1 Mode-locking versus number of sites in the interface
5.3.2 Mode-locking versus range of interaction
6 Conclusions and final remarks
References
Last updated: April 4th 1997
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