The $C^1$ property of convex carrying simplices for competitive maps

Abstract

For a class of competitive maps there is an invariant one-codimensional manifold (the carrying simplex) attracting all non-trivial orbits. In the present paper it is shown that its convexity implies that it is a $C^1$ submanifold-with-corners, neatly embedded in the non-negative orthant. The proof uses the characterization of neat embedding in terms of inequalities between Lyapunov exponents for ergodic invariant measures supported on the boundary of the carrying simplex.

18 pages, 5 figures; streamlined proofs, added figures. arXiv admin note: text overlap with arXiv:1709.08171

References in corpus (1)

• The $C^1$ property of convex carrying simplices for three-dimensional competitive maps

Cited by in corpus (1)

• Linearization and invariant manifolds on the carrying simplex for competitive maps