Dynamical systems on lattices with decaying interaction I: A functional analysis framework

摘要: Abstract We consider weakly coupled map lattices with a decaying interaction. That is, we systems which consist of phase space at every site such that the dynamics is little affected by far away sites. develop functional analysis framework formulates quantitatively decay interaction and able to deal sites are manifolds. This very well suited study systematically invariant objects. One obtains objects essentially local. use this prove stable manifold theorem show manifolds as smooth maps have properties (i.e. derivatives one coordinates respect small). Other applications structural stability close uncoupled possessing hyperbolic sets their sets, in companion paper Fontich et al. (2011) [10] .