Morse Functions Statistics
نویسنده
چکیده
We answer a question of V.I. Arnold concerning the growth rate of the number of Morse functions on the two sphere.
منابع مشابه
Investigation of analytical and numerical solutions for one-dimensional independent-oftime Schrödinger Equation
In this paper, the numerical solution methods of one- particale, one – dimensional time- independentSchrodinger equation are presented that allows one to obtain accurate bound state eigen values andeigen functions for an arbitrary potential energy function V(x). These methods included the FEM(Finite Element Method), Cooly, Numerov and others. Here we considered the Numerov method inmore details...
متن کاملRandom Morse Functions and Spectral Geometry
We study random Morse functions on a Riemann manifold (M, g) defined as random Fourier series of eigenfunctions of the Laplacian of the metric g. The randomness is determined by a fixed Schwartz function w and a small parameter ε > 0. We first prove that, as ε → 0, the expected distribution of critical values of this random function approaches a universal measure on R, independent of g, that ca...
متن کاملMorse-smale Characteristic in Circle-valued Morse Theory
In this paper we consider the φF category associated to the family of circle valued Morse functions defined on a closed manifold M . This number will be called the Morse-Smale characteristic of manifold M for circle-valued Morse functions and and it will be denoted by γs1(M). We present some basic notions and results concerning circle-valued Morse functions and we prove some properties for γs1(...
متن کاملComputing Optimal Discrete Morse Functions
The essential structural information of discrete Morse functions is captured by so-called Morse matchings. We show that computing optimal Morse matchings is NP-hard and give an integer programming formulation for the problem. Then we present first polyhedral results for the corresponding polytope and report on some preliminary computational results.
متن کاملMorse-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-...
متن کامل