The Morse Equation in the Conley Index Theory for Discrete Multivalued Dynamical Systems
نویسندگان
چکیده
A recent generalization of the Conley index to discrete multivalued dynamical systems without a continuous selector is motivated by applications data–driven dynamics. In present paper we continue program studying attractor–repeller pairs and Morse decompositions in this setting. particular, prove equation inequalities.
منابع مشابه
Conley Index for Discrete Multivalued Dynamical Systems
The deenitions of isolating block, index pair, and the Conley index, together with the proof of homotopy and additivity properties of the index are generalized for discrete multivalued dynamical systems. That generalization provides a theoretical background of numerical computation used by Mischaikow and Mrozek in their computer assisted proof of chaos in the Lorenz equations, where nitely repr...
متن کاملWeak Index Pairs and the Conley Index for Discrete Multivalued Dynamical Systems
Motivation to revisit the Conley index theory for discrete multivalued dynamical systems stems from the needs of broader real applications, in particular in sampled dynamics or in combinatorial dynamics. The new construction of the index in [B. Batko and M. Mrozek, SIAM J. Applied Dynamical Systems, 15(2016), pp. 1143-1162] based on weak index pairs, under the circumstances of the absence of in...
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 کاملConley index for random dynamical systems
Conley index theory is a very powerful tool in the study of dynamical systems, differential equations and bifurcation theory. In this paper, we make an attempt to generalize the Conley index to discrete random dynamical systems. And we mainly follow the Conley index for maps given by Franks and Richeson in [6]. Furthermore, we simply discuss the relations of isolated invariant sets between time...
متن کاملNovikov - Morse Theory for Dynamical Systems HuiJun
The present paper contains an interpretation and generalization of Novikov’s theory for Morse type inequalities for closed 1-forms in terms of concepts from Conley’s theory for dynamical systems. We introduce the concept of a flow carrying a cocycle α, (generalized) α-flow for short, where α is a cocycle in bounded Alexander-Spanier cohomology theory. Gradient-like flows can then be characteriz...
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 Dynamics and Differential Equations
سال: 2022
ISSN: ['1040-7294', '1572-9222']
DOI: https://doi.org/10.1007/s10884-022-10136-3