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Foliations by rigidity classes. (arXiv:1704.06328v1 [math.DS])

来源于:arXiv
For classical one-dimensional dynamical systems, such as circle diffeomorphisms, unimodal interval maps at the boundary of chaos, critical circle maps, the topological classes coincide with the rigidity classes. That is, the topological conjugacies are differentiable on the attractors. This phenomenon is known as rigidity. A natural question is now to investigate the rigidity phenomenon for more general dynamical systems. The situation is clearly more intricate. We cannot expect that the topological classes will always coincide with the rigidity classes, like in the classical context. See for example H\'enon maps at the boundary of chaos. Actually already for $C^3$ circle maps with a flat interval and Fibonacci rotation number the topological class is a $C^1$ co dimension $1$ manifold which is foliated by co dimension $3$ rigidity classes. The rigidity paradigm breaks, but in a very organized way. The foliations by rigidity classes will be an integral part of rigidity theory in general 查看全文>>