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The $C^{1}$ property of convex carrying simplices for competitive maps
Published online by Cambridge University Press: 17 October 2018
Abstract
For a class of competitive maps there is an invariant one-codimensional manifold (the carrying simplex) attracting all non-trivial orbits. In this 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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- © Cambridge University Press, 2018
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