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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>>