EVENT DETAILS AND ABSTRACT

Title: Normal forms on contracting foliations
Speaker: Boris Kalinin
Speaker Info: Penn State University
Brief Description:
Special Note: Midwest Dynamical Systems Conference
Abstract:

We consider a diffeomorphism $f$ of a compact manifold $M$ which contracts an invariant foliation $W$ with smooth leaves. If the differential of $f$ on $TW$ has narrow band spectrum, there exist coordinates $H _x : W_x \to T_x W$ in which $f_W(x)$ is a polynomial in a finite-dimensional Lie group $G$. We construct $H_x$ that depend smoothly on $x$ along the leaves of $W$ and give an atlas with transition maps in $G$. Our results apply, in particular, to any $C^1$-small perturbation of an algebraic systems. More generally, we construct similar normal forms on a stable foliation of an arbitrary measure preserving diffeomorphism $f$. This yields an $f$-invariant structure of a $G$ homogeneous space on almost every leaf.