Spatially Extended Circle Maps: Monotone Periodic Dynamics of Functions with Linear Growth

• DOI: 10.1007/s00332-003-0598-1
• Publication Date: 2004-03-09T16:44:20Z
• Authors: R. Coutinho; B. Fernandez
• Keywords: Rotation number; Dynamics

We introduce and study monotone periodic mappings acting on real functions with linear growth. These mappings represent the nonlinear dynamics of extended systems governed by a diffusive interaction and a periodic potential. They can be viewed as infinite-dimensional analogues of lifts of circle maps. Our results concern the existence and uniqueness of a rotation number and the existence of travelling waves. Moreover, we prove that the rotation number depends continuously on the mapping and we obtain a symmetry condition for this number to vanish. The results are applied to two classes of examples in population dynamics and in condensed matter physics.