robert ghrist

applied topology

click on the links to download preprints...

all versions are pre-publication drafts with eventual publication citations as listed

the author gratefully acknowledges the support of DARPA, the NSF, the AFOSR, and the ONR; of course, that doesn't mean they endorse what is written. neither does the university of pennsylvania. in fact, i don't think anyone except me and a few coauthors endorse the opinions expressed in these works. and even then, it's not a slam-dunk.

**DYNAMICS & BIFURCATIONS**

- [2010] R. Ghrist, J.B. Van den Berg, R. Vandervorst, and W. Wojcik, “Braid Floer homology,” submitted.
- [2009] S. Alexander, R. Bishop, and R. Ghrist, "Capture pursuit games on unbounded domains,"
*Ensiegn. Math.*, 55, 103-125. - [2009] R. Ghrist and R. Vandervorst, “Braids and parabolic scalar PDEs,''
*Transactions Amer. Math. Soc.*, 361, 2755-2788. - [2008] R. Ghrist, “Three examples of applied and computational homology,"
*Nieuw Archief voor Wiskunde*5/9(2). - [2008] J. Jung and R. Ghrist, “Pareto optimal multi-robot coordination with acceleration constraints,” in
*Proc. Intl. Conf. Robotics & Automation.* - [2007] R. Ghrist, “On the contact geometry and topology of ideal fluids,”
*Handbook of Mathematical Fluid Dynamics*, Vol. IV., 1-38. - [2006] R. Ghrist and R. Komendarczyk, “Overtwisted energy-minimizing curl eigenfields,”
*Nonlinearity*, 19(1), 41-52. - [2005] J. Etnyre and R. Ghrist, “Generic hydrodynamic instability for curl eigenfields,”
*SIAM J. Appl. Dynamical Systems*, 4(2), 377-390. - [2006] R. Ghrist “Braids and differential equations,'' in Proc. International Congress of Mathematicians, vol. III, 1-26.
- [2004] R. Ghrist and E. Kin, “Flowlines transervse to knot and link fibrations,”
*Pacific J. Math.*, 217(1), 61-86. - [2003] R. Ghrist, J.B.Van den Berg, and R.C. Vandervorst, “Morse theory on braids with applications to Lagrangian systems,”
*Invent. Math.*, 152(2), 369-432. - [2002] J. Etnyre and R. Ghrist, “Contact topology and hydrodynamics II: Solid tori,”
*Ergod. Thy. & Dyn. Sys.*, 22(3), 819-833. - [2002] J. Etnyre and R. Ghrist, “Contact topology and Anosov flows,”
*Top. & its Appl.*, 124 (2), 211-219. - [2002] R. Ghrist and D. Koditschek, “Safe cooperative robot dynamics on graphs,”
*SIAM J. Cont. & Opt.*, 40(5), 1556-1575. - [2002] R. Ghrist and R. Komendarczyk, “Topological features of inviscid flows,” in
*Introduction to the Geometry and Topology of Fluid Flows*, NATO-ASI Series II, vol. 47, Kluwer Press, 183-202. - [2001] J. Etnyre and R. Ghrist, “An index for closed orbits in Beltrami fields,”
*Physica D*, 159(3-4), 180-189. - [2001] R. Ghrist, “Steady nonintegrable high-dimensional fluids,”
*Lett. Math. Phys.*, 55(3), 193-204. - [2000] R. Ghrist, J.B.Vandenberg, and R.C. Vandervorst, “Closed characteristics of fourth-order twist systems via braids,”
*C. R. Acad. Sci. Paris Ser. I*, 331, 861- 865. - [2000] J. Etnyre and R. Ghrist,) “Contact topology and hydrodynamics III: knotted orbits,”
*Trans. Amer. Math. Soc.*, 352, 5781-5794. - [2000] R. Ghrist, “Resonant gluing bifurcations,”
*Intl. J. Bifurcation and Chaos*, 10(9), 2141-2160. - [2000] J. Etnyre and R. Ghrist, “Contact topology and hydrodynamics I: Beltrami fields and the Seifert Conjecture,”
*Nonlinearity*13, 441-458. - [2000] R. Ghrist, E. Klavins, and D. Koditschek, “Cyclic regulation of patterns,''
*Proc. Workshop on Algorithmic Foundations of Robotics*, B. Donald, K. Lynch, and D. Rus, eds., 205-220. - [1999] J. Etnyre and R. Ghrist, “Plane field flows,”
*Comment. Math. Helv.*, 74, 507-529. - [1999] J. Etnyre and R. Ghrist, “Construction of tight 3-manifolds via dynamics,”
*Proc. Amer. Math. Soc.*, 127, 3697-3706. - [1999] J. Etnyre and R. Ghrist, “Stratified integrals and unknots in inviscid flows,”
*Cont. Math*., 246,99-112. - [1999] R. Ghrist and D. Koditschek, “Safe Cooperative Robot Dynamics on Graphs,'' in
*Hybrid Systems and AI: Modeling, Analysis and Control of Discrete and Continuous Systems, AAAI*, SS-99-05, 65-70.

- [1998] R. Ghrist and T. Young, “From Morse-Smale to all links,”
*Nonlinearity*, 11, 1111-1125. - [1998] R. Ghrist, “Chaotic knots and wild dynamics”,
*Chaos, Solitons, and Fractals*, 9(4/5), 583-598. - [1997] R. Ghrist, P. Holmes, and M. Sullivan,
*Knots and Links in Three-Dimensional Flows*, Lecture Notes in Mathematics, Volume 1654, Springer-Verlag. - [1997] R. Ghrist, “Accumulations of infinite links,”
*Topology and its Applications*, 81, 171-184. - [1997] R. Ghrist, “Branched 2-manifolds supporting all links,”
*Topology*, 36(2), 423-438. - [1996] R. Ghrist and P. Holmes, “An ODE whose solutions contain all knots,”
*Intl. J. Bifurcation and Chaos*, 6(5), 779-800. - [1995] R. Ghrist, “Flows on S
^{3}supporting all links as orbits,”*Electronic Research Announcements of the AMS*, 1(2), 91-97. - [1994] R. Ghrist and P. Holmes, “Knotting within the gluing bifurcation,'' in
*IUTAM Symposium on Nonlinearity and Chaos in Engineering Dynamics*, J. M. T. Thompson and S. R. Bishop, Ed., John Wiley Press, 299-315. - [1993] R. Ghrist and P. Holmes, “Knots and orbit genealogies in three dimensional flows,'' in
*Bifurcations and Periodic Orbits of Vector Fields*, NATO ASI Series C, Volume 408, Kluwer Academic Publishers, 185-239.