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arXiv · 1801.01032

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

Janusz Mierczyński
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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.

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Janusz Mierczyński. 2018-01-01. The $C^1$ property of convex carrying simplices for competitive maps. https://doi.org/10.1017/etds.2018.85

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