Abstract
The possibility of an a priori complete description of finite-parameter models including systems with structurally unstable Poincaré homoclinic curves is studied. The main result reported here is that systems having a countable set of moduli of ω-equivalence and systems having infinitely many degenerate periodic and homoclinic orbits are dense in the Newhouse regions of ω-non-stability. We discuss the question of correctly setting a problem for the analysis of models of such type.
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