Conley index theory without index pairs. I: The point-set level theory
نویسندگان
چکیده
We propose a new framework for Conley index theory. The main feature of our approach is that we do not use the notion pairs. introduce, instead, notions compactifiable subsets and neighbourhoods, formulate prove basic results in theory using these notions. treat both discrete time case continuous case.
منابع مشابه
Efficient Automation of Index Pairs in Computational Conley Index Theory
We present new methods of automating the construction of index pairs, essential ingredients of discrete Conley index theory. These new algorithms are further steps in the direction of automating computer-assisted proofs of semiconjugacies from a map on a manifold to a subshift of finite type. We apply these new algorithms to the standard map at different values of the perturbative parameter ε a...
متن کاملConley Index Theory and Novikov-Morse Theory
We derive general Novikov-Morse type inequalities in a Conley type framework for flows carrying cocycles, therefore generalizing our results in [FJ2] derived for integral cocycle. The condition of carrying a cocycle expresses the nontriviality of integrals of that cocycle on flow lines. Gradient-like flows are distinguished from general flows carrying a cocycle by boundedness conditions on thes...
متن کاملThe Conley Index, Gauge Theory, and Triangulations
This is an expository paper about Seiberg-Witten Floer stable homotopy types. We outline their construction, which is based on the Conley index and finite dimensional approximation. We then describe several applications, including the disproof of the high-dimensional triangulation conjecture.
متن کاملConnecting Fast-slow Systems and Conley Index Theory via Transversality
Geometric Singular Perturbation Theory (GSPT) and Conley Index Theory are two powerful techniques to analyze dynamical systems. Conley already realized that using his index is easier for singular perturbation problems. In this paper, we will revisit Conley’s results and prove that the GSPT technique of Fenichel Normal Form can be used to simplify the application of Conley index techniques even ...
متن کاملThe Conley Index and Global Bifurcations, Part I: Concepts and Theory
The Morse index is deened for a hyperbolic equilibrium point of a vector eld as the dimension of its unstable manifold. This paper presents the theory of the Conley index, which is a far-reaching generalization of the Morse index. It also outlines how this new index can be used to solve global bifurcation problems. In fact, we shall argue that the Conley index methods constitute the most approp...
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: Journal of Fixed Point Theory and Applications
سال: 2022
ISSN: ['1661-7746', '1661-7738']
DOI: https://doi.org/10.1007/s11784-022-01037-5