In some invertible maps of the plane that depend on a parameter, boundaries of basins of attraction are extremely sensitive to small changes in the parameter. A basin boundary can jump suddenly, and, as it does, change from being smooth to fractaL Such changes are called basin boundary metamorphoses. We prove (under certain non-degeneracy assumptions) that a metamorphosis occurs when the stable and unstable manifolds of a periodic saddle on the boundary undergo a homoclinic tangency.
ALLIGOOD K., T., TEDESCHINI LALLI, L., Yorke, J.A. (1991). Metamorphoses: Sudden jumps in Basin Boundaries. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 141, 1-8 [10.1007/BF02100002].
Metamorphoses: Sudden jumps in Basin Boundaries
TEDESCHINI LALLI, Laura;
1991-01-01
Abstract
In some invertible maps of the plane that depend on a parameter, boundaries of basins of attraction are extremely sensitive to small changes in the parameter. A basin boundary can jump suddenly, and, as it does, change from being smooth to fractaL Such changes are called basin boundary metamorphoses. We prove (under certain non-degeneracy assumptions) that a metamorphosis occurs when the stable and unstable manifolds of a periodic saddle on the boundary undergo a homoclinic tangency.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
