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Hyperbolicity of infinite-dimensional drift systems

The authors study the stability of trajectories in infinite-dimensional systems which are perturbations of infinite chains of independent finite-dimensional systems with strongly hyperbolic properties. They consider a special 'drift' type of perturbation in which a system with number n interacts only with systems with previous numbers. They reduce the problem of stability to a problem of small perturbations in a special space with an appropriate metric and construct the corresponding version of perturbation theory. Their main result is to show that the type of hyperbolicity can be radically changed when the parameters of the system grow.