**Robust cycles and tangencies of large codimension
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This talk is concerned with the construction of robust cycles and (large) tangencies in partially hyperbolic diffe- omorphisms. We provide new methods to construct robust heterodimensional cycles and tangencies in dimension d >4 . To construct heterodimensional cycles we use blenders that are not necessarily expanding or contracting along the central direction. This allows us to construct also robust equidimensional cycles, i.e., cycles associated with different hyperbolic sets of the same index (or co-index zero). These constructions of cycles will be also used to obtain tangencies. Namely, we will get robust tangencies by means of equidimensional/heterodimensional cycles constructed in the tangent bundle. The known methods to construct robust tangencies are limited to the codimen- sion one (non-degenerated) case and are done using fat hyperbolic sets (thick horseshoes or blenders) in the ambient manifold.

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**Joint work with Artem Raibekas (UFF) http://arxiv.org/abs/1509.05325