@inbook{714649a2278946b487b39b16690e2ede,

title = "Transient Chaos in Spatially Extended Systems",

abstract = "Chaos is not restricted to systems without any spatial extension: it in fact occurs commonly in spatially extended dynamical systems that are most typically described by nonlinear partial differential equations (PDEs). If the patterns generated by such a system change randomly in time, we speak of spatiotemporal chaos, a kind of temporally chaotic pattern-forming process. If, in addition, the patterns are also spatially irregular, there is fully developed spatiotemporal chaos. In principle, the phase-space dimension of a spatially extended dynamical system is infinite. However, in practice, when a spatial discretization scheme is used to solve the PDE, or when measurements are made in a physical experiment with finite spatial resolution, the effective dimension of the phase space is not infinite but still high.",

keywords = "Chaotic Attractor, Dimension Density, Escape Rate, Lyapunov Exponent, Stable Manifold",

author = "Ying-Cheng Lai and Tam{\'a}s T{\'e}l",

year = "2011",

month = jan,

day = "1",

doi = "10.1007/978-1-4419-6987-3_9",

language = "English (US)",

series = "Applied Mathematical Sciences (Switzerland)",

publisher = "Springer",

pages = "311--339",

booktitle = "Applied Mathematical Sciences (Switzerland)",

}