Topological Fiber Entropy for Linear Flows on Vector Bundles

Abstract

For linear flows on vector bundles, it is shown that the topological entropy of lower dimensional subspaces in the fibers is determined by the Morse spectrum over chain recurrent components of the induced flows on Grassmann bundles.

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Acknowledgments

F. Colonius is supported by DFG grant Co 124/17-2 within DFG Priority Program 1305 Control Theory of Digitally Networked Dynamical Systems. L.A.B. San Martin is supported by CNPq grant n o 303755/2009-1 and FAPESP grant n o 07/06896-5. A.J. da Silva is supported by CAPES grant n o 4229/10-0.

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Correspondence to Fritz Colonius.

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Colonius, F., San Martin, L.A. & da Silva, A.J. Topological Fiber Entropy for Linear Flows on Vector Bundles. J Dyn Control Syst 20, 475–490 (2014). https://doi.org/10.1007/s10883-014-9217-8

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Keywords

  • Topological entropy
  • Linear flows
  • Bilinear control systems

Mathematics Subject Classification 2010

  • 37B40
  • 37H15