Conley index for discrete multi-valued dynamical systems
نویسندگان
چکیده
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 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 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 کاملRobust Control of Set-Valued Discrete-Time Dynamical Systems
This paper presents results obtained for the control of set-valued discrete-time dynamical systems. Such systems model nonlinear systems subject to persistent bounded noise. A robust control problem for such systems is introduced. The problem is formulated as a dynamic game, wherein the controller plays against the set-valued system. Both necessary and sufficient conditions in terms of (station...
متن کاملThe Conley index for fast-slow systems II: Multi-dimensional slow variable
We use Conley index theory to develop a general method used to prove existence of periodic and heteroclinic orbits in a singularly perturbed system of ODE’s. This is a continuation of the authors’ earlier work [9] which Supported by NSF Grant INT-0089631 and by JSPS Japan-U.S. Cooperative Science Program. Partially supported by NSF EIA-BITS grant 426411. Partially supported by Grant-in-Aid for ...
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: Topology and its Applications
سال: 1995
ISSN: 0166-8641
DOI: 10.1016/0166-8641(94)00088-k