The Connection Matrix in Morse-Smale Flows II
نویسندگان
چکیده
منابع مشابه
The Morse-Smale Complex
The main aim of this paper is to present the construction of the Morse– Smale complex of a compact smooth manifold M with boundary and to establish the connection to the topology of M . This approach to connecting the analysis of an appropriate function f : M → R — respectively the dynamical system associated to such a function and a Riemannian metric g — with the topology of the manifold was i...
متن کاملThe Connection Matrix Theory for Morse Decompositions
The connection matrix theory for Morse decompositions is introduced. The connection matrices are matrices of maps between the homology indices of the sets in the Morse decomposition. The connection matrices cover, in a natural way, the homology index braid of the Morse decomposition and provide information about the structure of the Morse decomposition. The existence of connection matrices of M...
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 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 کاملPractical Considerations in Morse-Smale Complex Computation
The Morse-Smale complex is an effective topology-based representation for identifying, ordering, and selectively removing features in scalar-valued data. Several algorithms are known for its effective computation, however, common problems pose practical challenges for any feature-finding approach using the Morse-Smale complex. We identify these problems and present practical solutions: (1) we i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1995
ISSN: 0002-9947
DOI: 10.2307/2154924