竞争映射的凸承载单形的$C^1$性质
The $C^1$ property of convex carrying simplices for competitive maps
摘要：
对于一类竞争映射，存在吸引所有非平凡轨道的不变一维余维流形（携带单形）。在本文中，它表明，它的凸性意味着它是一个$C^1$子流形与角，整齐地嵌入在非负正交。证明使用整洁嵌入的表征之间的不等式的李雅普诺夫指数遍历不变测度支持的边界上携带的单纯形。
英文摘要：
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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