Abstract
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.
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Coutinho, R., Fernandez, B. Spatially Extended Circle Maps: Monotone Periodic Dynamics of Functions with Linear Growth. J Nonlinear Sci 14, 93–118 (2004). https://doi.org/10.1007/s00332-003-0598-1
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DOI: https://doi.org/10.1007/s00332-003-0598-1