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Controlling homoclinic orbits
 A. M. Bloch,
 J. E. Marsden
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In this paper we analyze various controltheoretic aspects of a nonlinear control system possessing homoclinic or heteroclinic orbits. In particular, we show that for a certain class of nonlinear control system possessing homoclinic orbits, a control can be found such that the system exhibits arbitrarily long periods in a neighborhood of the homoclinic. We then apply these ideas to bursting phenomena in the near wall region of a turbulent boundary layer. Our analysis is based on a recently developed finitedimensional model of this region due to Aubry, Holmes, Lumley, and Stone.
Communicated by John Lumley
The research of A.M. Bloch was partially supported by the U.S. Army Research Office through MSI at Cornell University and by NSF Grant DMS8701576 and AFOSR Grant AFOSRISSA870077, J.E. Marsden's research was partially supported by DOE Contract DEATO388ER12097 and MSI at Cornell University and by AFOSR Contract No. 88NA321.
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 Title
 Controlling homoclinic orbits
 Journal

Theoretical and Computational Fluid Dynamics
Volume 1, Issue 3 , pp 179190
 Cover Date
 19890501
 DOI
 10.1007/BF00417919
 Print ISSN
 09354964
 Online ISSN
 14322250
 Publisher
 SpringerVerlag
 Additional Links
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 Authors

 A. M. Bloch ^{(1)} ^{(2)}
 J. E. Marsden ^{(3)} ^{(4)}
 Author Affiliations

 1. MSI, Cornell University, 14853, Ithaca, NY, USA
 2. Department of Mathematics, Ohio State University, 43210, Columbus, OH, USA
 3. Department of Mathematics, University of California, 94720, Berkeley, CA, USA
 4. Cornell University, 148537901, Ithaca, NY, USA