Results 171 to 180 of about 5,574,136 (208)
Diffeomorphisms Preserving Morse–Bott Functions [PDF]
Indagationes Mathematicae, 2020 Let $f:M\to\mathbb{R}$ be a Morse-Bott function on a closed manifold $M$, so the set $Σ_f$ of its critical points is a closed submanifold whose connected components may have distinct dimensions. Denote by $\mathcal{S}(f) = \{h \in \mathcal{D}(M) \mid f\circ h=h \}$ the group of diffeomorphisms of $M$ preserving $f$ and let $\mathcal{D}(Σ_f)$ be the ...
Sergiy Maksymenko
exaly +4 more sources
Some of the next articles are maybe not open access.
Related searches:
Related searches:
Normal Morse Data of Two Morse Functions
1988In this chapter we analyze the normal Morse data at a critical point p∈Z of a function f1: Z → ℝ under the assumption that there exists a second function f2: Z → ℝ such that the map (f1,f2): Z → ℝ2 has a nondegenerate critical point at p (see below).
Mark Goresky, Robert MacPherson
openaire +1 more source
On morse theory for piecewise smooth functions
Journal of Dynamical and Control Systems, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Agrachev, A. A. +2 more
openaire +2 more sources
Morse numbers and minimal morse functions on nonsimply connected manifolds
Ukrainian Mathematical Journal, 1988See the review in Zbl 0648.58005.
openaire +1 more source
2004
In this chapter we introduce the Morse-Smale transversality condition for gradient vector fields, and we prove the Kupka-Smale Theorem (Theorem 6.6) which says that the space of smooth Morse-Smale gradient vector fields is a dense subspace of the space of all smooth gradient vector fields on a finite dimensional compact smooth Riemannian manifold (M,g)
Augustin Banyaga, David Hurtubise
openaire +1 more source
In this chapter we introduce the Morse-Smale transversality condition for gradient vector fields, and we prove the Kupka-Smale Theorem (Theorem 6.6) which says that the space of smooth Morse-Smale gradient vector fields is a dense subspace of the space of all smooth gradient vector fields on a finite dimensional compact smooth Riemannian manifold (M,g)
Augustin Banyaga, David Hurtubise
openaire +1 more source
The Periodicity of Morse's Function
Physical Review, 1935The applicability of a simple modification of Morse's rule has been tested, and found generally satisfactory for simple non-hydride di-atoms and for hydrides of the $K\mathrm{H}$ period. Morse's function is shown to possess a periodic character, and to be capable of adjustment by the introduction of group numbers and period constants on the basis of ...
openaire +1 more source
1988
It is often necessary to consider a “Morse function” f: X → ℝ which is not proper, but which can be extended to a proper function $$ \bar{f}:Z \to \mathbb{R} $$ where Z contains X as a dense open subset. For example, Z may be a compactification of some noncompact algebraic variety X ⊂ ℂℙ n , and f may be a smooth function defined on the ambient ...
Mark Goresky, Robert MacPherson
openaire +1 more source
It is often necessary to consider a “Morse function” f: X → ℝ which is not proper, but which can be extended to a proper function $$ \bar{f}:Z \to \mathbb{R} $$ where Z contains X as a dense open subset. For example, Z may be a compactification of some noncompact algebraic variety X ⊂ ℂℙ n , and f may be a smooth function defined on the ambient ...
Mark Goresky, Robert MacPherson
openaire +1 more source
The Topology of Morse Functions
2011The present chapter is the heart of Morse theory, which is based on two fundamental principles. The “weak” Morse principle states that as long as the real parameter t varies in an interval containing only regular values of a smooth function \(f : M \rightarrow \mathbb{R}\), the topology of the sublevel set {f ≤ t} is independent of t.
openaire +1 more source
A program for normalised morse functions
Computer Physics Communications, 1972J.R. Parkinson, D.T. Birtwistle
openaire +1 more source