INVARIANT MANIFOLDS FOR COMPETITIVE DISCRETE SYSTEMS IN THE PLANE
INVARIANT MANIFOLDS FOR COMPETITIVE DISCRETE SYSTEMS IN THE PLANE
Let $T$ be a competitive map on a rectangular region $\mathcal{R}\subset \mathbb{R}^2$, and assume $T$ is $C^1$ in a neighborhood of a fixed point $\bar{\rm x}\in \mathcal{R}$. The main results of this paper give conditions on $T$ that guarantee the existence of an invariant curve emanating from $\bar{\rm x}$ when …