On models with non-rough Poincaré homoclinic curves. (English) Zbl 0783.58049
Summary: 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 \(\Omega\)-equivalence and systems having infinitely many degenerate periodic and homoclinic orbits are dense in the Newhouse regions of \(\Omega\)-non-stability. We discuss the question of correctly setting a problem for the analysis of models of such type.
MSC:
| 37G99 | Local and nonlocal bifurcation theory for dynamical systems |
References:
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