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- William D. Kalies, Konstantin Mischaikow, Robert C. A. M. VanderVorst
- Foundations of Computational Mathematics
- 2005

In this paper we give a new definition of the chain recurrent set of a continuous map using finite spatial discretizations. This approach allows for an algo-rithmic construction of isolating blocks for the components of Morse decompositions which approximate the chain recurrent set arbitrarily closely as well as discrete approximations of Conley's Lyapunov… (More)

- T. O. Rot, R. C. A. M. Vandervorst, A. M. Vandervorst
- 2013

For Morse-Smale pairs on a smooth, closed manifold the Morse-Smale-Witten chain complex can be defined. The associated Morse homol-ogy is isomorphic to the singular homology of the manifold and yields the classical Morse relations for Morse functions. A similar approach can be used to define homological invariants for isolated invariant sets of flows on a… (More)

- William D. Kalies, Konstantin Mischaikow, Robert C. A. M. VanderVorst
- Foundations of Computational Mathematics
- 2016

The algebraic structure of the attractors in a dynamical system determine much of its global dynamics. The collection of all attractors has a natural lattice structure, and this structure can be detected through attracting neighborhoods, which can in principle be computed. Indeed, there has been much recent work on developing and implementing general… (More)

- ROBERT VANDERVORST, Jan Bouwe VandenBerg
- 2010

Floer homology is a powerful variational technique used in Symplectic Geometry to derive a Morse type theory for the Hamiltonian action functional. In two and three dimensional dynamics the topological structures of braids and links can used to distinguish between various types of periodic orbits. Various classes of braids are introduced and Floer type… (More)

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