LAUSR.org creates dashboard-style pages of related content for over 1.5 million academic articles. Sign Up to like articles & get recommendations!

Surgery for partially hyperbolic dynamical systems II. Blow-up of a complex curve

Photo from wikipedia

In this paper we use the blow-up surgery introduced in [ 1 ] to produce new higher dimensional partially hyperbolic flows. The main contribution of the paper is the slow-down construction… Click to show full abstract

In this paper we use the blow-up surgery introduced in [ 1 ] to produce new higher dimensional partially hyperbolic flows. The main contribution of the paper is the slow-down construction which accompanies the blow-up construction . This new ingredient allows to dispose of a rather strong domination assumption which was crucial for results in [ 1 ]. Consequently we gain more flexibility which allows to construct new volume-preserving partially hyperbolic flows as well as new examples which are not fiberwise Anosov. The latter are produced by starting with the geodesic flow on complex hyperbolic manifold which admits a totally geodesic complex curve. Then by performing the slow-down first and the blow-up second we obtain a new (volume-preserving) partially hyperbolic flows.

Keywords: hyperbolic flows; blow; partially hyperbolic; complex curve; surgery

Journal Title: Mathematische Zeitschrift
Year Published: 2019

Link to full text (if available)


Share on Social Media:                               Sign Up to like & get
recommendations!

Related content

More Information              News              Social Media              Video              Recommended



                Click one of the above tabs to view related content.