Connection Matrices in Combinatorial Topological Dynamics

Marian Mrozek has been a Professor of Mathematics at Jagiellonian University in Krakow since 1999. He has worked in the area of computational dynamics throughout this time, with an early emphasis on Conley index. He was one of the first researchers to rigorously establish chaotic dynamics in the Lorenz attractor, using Conley index techniques in combination with computer-assisted proof techniques. In addition, he co-authored one of the first books on Computational Homology, which was published by Springer Verlag in 2004.Thomas Wanner has been a Professor of Mathematics at George Mason University since 2002. His research focus lies in the areas of dynamics and computational topology. He has worked both on applied problems such as the analysis of microstructures generated via phase separation in metal alloys, as well as on theoretical results in infinite-dimensional dynamics and Conley index techniques in combinatorial dynamics. He has contributed a chapter to the book "Dynamics Reported 4" which was published by Springer Verlag in 1995. Since its inception, he has been a member of the editorial board of the Springer book series "Frontiers in Applied Dynamical Systems."

• Preface.- Introduction.- Main Results.- Preliminaries.- Poset Filtered Chain Complexes.- Algebraic Connection Matrices.- Connection Matrices in Lefschetz Complexes.- Dynamics of Combinatorial Multivector Fields.- Connection Matrices for Forman's Gradient Vector Fields.- Future Work and Open Problems.- References.