Local Parameter Identifiability: Case of Discrete Infinite-Dimensional Parameter

In this paper, we study the problem of local parameter identifiability for discrete dynamical systems with discrete infinite-dimensional parameter. Our results are related to the so-called conditional local parameter identifiability. In this case, one introduces a special class \(\mathcal{P}\) $\mathcal{P}$ of possible perturbations of the selected parameter \(P^0\) $P^0$ and finds conditions on observations of trajectories under which all parameters \(P\in \mathcal{P}\) $P\in \mathcal{P}$ close to \(P^0\) $P^0$ coincide with \(P^0\) $P^0$ . We consider discrete dynamical systems for which the trajectories are observed at points \(k=1,2,\dots \) $k=1,2,\cdots$ or at a countable set of points \(0<t_1<t_2<\dots \) $0<t_1<t_2<\cdots$ . The case of a linearly perturbed diffeomorphism in a neighborhood of a hyperbolic set is also considered.