Linearization and invariant manifolds on the carrying simplex for competitive maps. (English) Zbl 1436.37041
The authors prove that the restriction of the competitive map to the carrying simplex in a neighborhood of an interior fixed point is topologically conjugate to the restriction of the map to its pseudo-unstable manifold by an invariant foliation. The results are related to Hirsch’s problem regarding the smoothness of the carrying simplex.
Reviewer: Gheorghe Tigan (Timisoara)
MSC:
| 37D10 | Invariant manifold theory for dynamical systems |
| 37C05 | Dynamical systems involving smooth mappings and diffeomorphisms |
| 37C15 | Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems |
| 37C25 | Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics |
Keywords:
carrying simplex; invariant foliation; pseudo-stable manifold; pseudo-unstable manifold; linearization; invariant manifoldReferences:
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