Dr. William Kalies

• An algorithmic approach to lattices and order in dynamics
  SIAM Journal on Applied Dynamical Systems 17, pp. 1617–1649, 2018.
  With D. Kasti and R.C.A.M. van der Vorst.

 

• Analytic continuation of local (un)stable manifolds with rigorous computer-assisted error bounds
  SIAM Journal on Applied Dynamical Systems 17, pp. 157-202, 2018.
  With S. Kepley and J.D. Mireles-James

 

• Lattice structures for attractors II
  Foundations of Computational Mathematics 16, pp. 1151-1191, 2016
  With K. Mischaikow and R.C.A.M. van der Vorst.

 

• Chaos near a resonant inclination-flip   
  Physica D: Nonlinear Phenomena 334, pp. 141-157, 2016.
  With M. Fontaine and V. Naudot.

 

• Efficient computation of Lyapunov functions for Morse decompositions   
  Discrete and Continuous Dynamical Systems 20, pp. 2419-2451, 2015.
  With A. Goullet, S. Harker, D. Kasti, and K. Mischaikow.

 

• Lattice structures for attractors I   
  Journal of Computational Dynamics 1, pp. 307-338, 2014.
  With K. Mischaikow and R.C.A.M. van der Vorst.

 

• A reinjected cuspidal horseshoe   
  Discrete and Continuous Dynamical Systems, (Supp. 2013), 227-236, 2013.
  With M. Fontaine and V. Naudot.

 

• Rigorous computation of the global dynamics of integrodifference equations with smooth nonlinearities   
  SIAM Journal on Numerical Analysis 51, pp. 2957-2983, 2013.
  With S. Day.

 

• A database schema for the analysis of global dynamics of multiparameter systems   
  SIAM Journal on Applied Dynamical Systems 8, pp. 757-789, 2009.
  With Z. Arai, H. Kokubu, K. Mischaikow, H. Oka, and P. Pilarczyk.

 

• Topological horseshoes of traveling waves for a fast-slow predator-prey system
  Journal of Dynamics and Differential Equations 19, pp. 623-654, 2007.
  With M. Gameiro, T. Gedeon, H. Kokubu, K. Mischaikow, and H. Oka.

 

• Polygonal approximation of flows
  Topology and Its Applications 154, pp. 2501-2520, 2007.
  With E. Boczko and K. Mischaikow.

 

• A computational approach to Conley's decomposition theorem   
  Journal of Computational and Nonlinear Dynamics 1, pp. 312-319, 2006.
  With H. Ban.

 

• An algorithmic approach to chain recurrence
  Foundations of Computational Mathematics 5, pp. 409-449, 2005.
  With K. Mischaikow and R.C.A.M. van der Vorst.

For software and overviews of research projects visit the    CHomP: Computational Homology Project  

• chom - a cubical homology program

Theory and Algorithms

• Verified homology computations for nodal domains 
  Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 7, pp. 1695-1726, 2009.
  With S. Day and T. Wanner.

 

• Probabilistic and numerical validation of homology computations for nodal domains
  Electronic Research Announcements of the American Mathematical Society 13, pp. 60-73, 2007.
  With S. Day, K. Mischaikow, and T. Wanner.

 

• Topological characterization of spatial-temporal chaos
  Physical Review E 70, Article 035203 (Rapid communication), 2004.
  With M. Gameiro and K. Mischaikow.

 

• Cubical approximation and computation of homology
  Banach Center Publications 47, pp. 115-131, 1999.
  With K. Mischaikow and G. Watson.

 Applications

• Three-dimensional analysis of solid oxide fuel cell Ni-YSZ anode interconnectivity
  Microscopy and Microanalysis 15, pp. 71-77, 2009.
  With J.R. Wilson, M. Gameiro, K. Mischaikow, P. Voorhees, and S.A. Barnett.

 

• On the detection of simple points in higher dimensions using cubical homology
  IEEE Transactions on Image Processing 15(8), pp. 2462-2469, 2006.
  With M. Niethammer, K. Mischaikow, and A. Tannenbaum.

 

• Analysis of blood vessel topology by cubical homology
  Proceedings of International Conference on Imagine Processing 2002, vol 2, pp. 969-972, 2002.
  With M. Niethammer, A.N. Stein, P. Pilarczyk, K. Mischaikow, and A. Tannenbaum.

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