We study fixed point theorems for maps which satisfy a property of stretching a suitably oriented topological space Z along the paths connecting two disjoint subsets of Z. Our results reconsider and extend previous theorems in [56, 59, 60] where the case of two-dimensional cells (that is topological spaces homeomorphic to a rectangle of the plane) was analyzed. Applications are given to topological horseshoes and to the study of the periodic points and the symbolic dynamics associated to discrete (semi)dynamical systems.
Papini, D., Zanolin, F. (2007). Some results on periodic points and chaotic dynamics arising from the study of the nonlinear Hill equations. In Subalpine Rhapsody in Dynamics (pp.115-157).
Some results on periodic points and chaotic dynamics arising from the study of the nonlinear Hill equations
PAPINI, DUCCIO;
2007-01-01
Abstract
We study fixed point theorems for maps which satisfy a property of stretching a suitably oriented topological space Z along the paths connecting two disjoint subsets of Z. Our results reconsider and extend previous theorems in [56, 59, 60] where the case of two-dimensional cells (that is topological spaces homeomorphic to a rectangle of the plane) was analyzed. Applications are given to topological horseshoes and to the study of the periodic points and the symbolic dynamics associated to discrete (semi)dynamical systems.
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https://hdl.handle.net/11365/37577
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