6533b7dbfe1ef96bd12712e4

RESEARCH PRODUCT

Partially hyperbolic diffeomorphisms on Heisenberg nilmanifolds and holonomy maps

Yi ShiYi Shi

subject

Transitive relationPure mathematicsMathematics::Dynamical SystemsMathematical analysisHolonomyGeneral MedicineAutomorphismSet (abstract data type)CorollaryChain (algebraic topology)AttractorMathematics::Differential GeometryNilmanifoldMathematics::Symplectic GeometryMathematics

description

Abstract In this note we show that all partially hyperbolic automorphisms on a 3-dimensional non-Abelian nilmanifold can be C 1 -approximated by structurally stable C ∞ -diffeomorphisms, whose chain recurrent set consists of one attractor and one repeller. In particular, all these partially hyperbolic automorphisms are not robustly transitive. As a corollary, the holonomy maps of the stable and unstable foliations of the approximating diffeomorphisms are twisted quasiperiodically forced circle homeomorphisms, which are transitive but non-minimal and satisfy certain fiberwise regularity properties.

yearjournalcountryeditionlanguage
2014-09-01Comptes Rendus Mathematique
https://doi.org/10.1016/j.crma.2014.07.002