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On the growth sequence for symplectically hyperbolic manifolds

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Abstract

We study the growth rate of a sequence which measures the uniform norm of the differential under the iterates of maps. On symplectically hyperbolic manifolds, we show that this sequence has at least linear growth for every non-identical symplectomorphisms which are symplectically isotopic to the identity.

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References

  1. A. Floer, Morse theory for Lagrangian intersections, Journal of Differential Geometry 28 (1988), 513–547.

    MathSciNet  MATH  Google Scholar 

  2. M. Gromov, Kähler hyperbolicity and L 2-Hodge theory, Journal of Differential Geometry 33 (1991), 263–292.

    MathSciNet  MATH  Google Scholar 

  3. M. Gromov, Asymptotic invariants of infinite groups, in Geometric Group Theory II, London Mathematical Society Lecture Notes, Vol. 182, Cambridge University Press, 1993.

  4. J. Kędra, Symplectically hyperbolic manifolds, Differential Geometry and its Applications 27 (2009), 455–463.

    Article  MathSciNet  MATH  Google Scholar 

  5. D. McDuff and D. Salamon, Introduction to Symplectic Topology, Oxford Mathematical Monographs, Oxford University Press, New York, 1998.

    MATH  Google Scholar 

  6. L. Polterovich, Growth of maps, distortion in groups and symplectic geometry, Inventiones Mathematicae 150 (2002), 655–686.

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Schwarz, On the action spectrum for closed symplectically aspherical manifolds, Pacific Journal of Mathematics 193 (2000), 419–461.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Center for Geometry and Physics, Institute for Basic Science, 77 Cheongam-ro, Nam-gu, Pohang-si, Gyeongsangbuk-do, Korea, 790-784

    Youngjin Bae

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  1. Youngjin Bae
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Correspondence to Youngjin Bae.

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Bae, Y. On the growth sequence for symplectically hyperbolic manifolds. Isr. J. Math. 204, 417–430 (2014). https://doi.org/10.1007/s11856-014-1103-2

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  • DOI: https://doi.org/10.1007/s11856-014-1103-2

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