A spectral gap for a one-dimensional lattice of coupled piecewise expanding interval maps
Keller G, Liverani C (2005)
Publication Type: Book chapter / Article in edited volumes
Publication year: 2005
Publisher: Springer
Edited Volumes: Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems, Lecture Notes in Physics
Series: Lecture Notes in Physics
City/Town: Heidelberg
Book Volume: 671
Pages Range: 115-151
ISBN: 978-3-540-24289-5
DOI: 10.1007/11360810_6
Abstract
We study one-dimensional lattices of weakly coupled piecewise expanding interval maps as dynamical systems. Since neither the local maps need to have full branches nor the coupling map needs to be a homeomorphism of the infinite dimensional state space, we cannot use symbolic dynamics or other techniques from statistical mechanics. Instead we prove that the transfer operator of the infinite dimensional system has a spectral gap on suitable Banach spaces generated by measures with marginals that have densities of bounded variation. This implies in particular exponential decay of correlations in time and space.
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APA:
Keller, G., & Liverani, C. (2005). A spectral gap for a one-dimensional lattice of coupled piecewise expanding interval maps. In Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems, Lecture Notes in Physics. (pp. 115-151). Heidelberg: Springer.
MLA:
Keller, Gerhard, and Carlangelo Liverani. "A spectral gap for a one-dimensional lattice of coupled piecewise expanding interval maps." Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems, Lecture Notes in Physics. Heidelberg: Springer, 2005. 115-151.
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