Dynamically ordered energy function for Morse-Smale diffeomorphisms on 3-manifolds

Self-indexing energy function for Morse-Smale diffeomorphisms on 3-manifolds

The paper is devoted to finding conditions to the existence of a self-indexing energy function for Morse-Smale diffeomorphisms on a 3manifold M3. These conditions involve how the stable and unstable manifolds of saddle points are embedded in the ambient manifold. We also show that the existence of a self-indexing energy function is equivalent to the existence of a Heegaard splitting of M3 of a ...

The Dynamics of Morse-smale Diffeomorphisms on the Torus

For orientation preserving diffeomorphisms on the torus necessary and sufficient conditions are given for an isotopy class to admit a Morse-Smale diffeomorphism with a specified periodic behavior. The Morse-Smale diffeomorphisms have been shown to be exactly the structurally stable diffeomorphisms with finite nonwandering set [8]. Several recent papers have analyzed the relationship between the...

Hierarchical Morse - Smale Complexes for Piecewise Linear 2-Manifolds

We present algorithms for constructing a hierarchy of increasingly coarse Morse-Smale complexes that decompose a piecewise linear 2-manifold. While these complexes are defined only in the smooth category, we extend the construction to the piecewise linear category by ensuring structural integrity and simulating differentiability. We then simplify Morse-Smale complexes by canceling pairs of crit...

Morse-Smale Regression.

This paper introduces a novel partition-based regression approach that incorporates topological information. Partition-based regression typically introduce a quality-of-fit-driven decomposition of the domain. The emphasis in this work is on a topologically meaningful segmentation. Thus, the proposed regression approach is based on a segmentation induced by a discrete approximation of the Morse-...

Transitive Partially Hyperbolic Diffeomorphisms on 3-Manifolds