The $C^1$ property of convex carrying simplices for competitive maps
Dynamical Systems
2020-05-27 v2 Classical Analysis and ODEs
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 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.
Keywords
Cite
@article{arxiv.1801.01032,
title = {The $C^1$ property of convex carrying simplices for competitive maps},
author = {Janusz Mierczyński},
journal= {arXiv preprint arXiv:1801.01032},
year = {2020}
}
Comments
18 pages, 5 figures; streamlined proofs, added figures. arXiv admin note: text overlap with arXiv:1709.08171