Discrete-time systems with countably many but more than one omega-limit sets admit no continuous one-to-one immersion into finite-dimensional linear systems.
Learning Koopman Eigenfunctions and Invariant Subspaces From Data: Symmetric Subspace Decomposition
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On the Nonexistence of Continuous Immersions for Discrete-time Systems
Discrete-time systems with countably many but more than one omega-limit sets admit no continuous one-to-one immersion into finite-dimensional linear systems.