Journal of Symplectic Geometry

On the growth rate of Leaf-Wise intersections

Leonardo Macarini, Will J. Merry, and Gabriel P. Paternain

Full-text: Open access

Abstract

We define a new variant of Rabinowitz Floer homology that is particularly well suited to studying the growth rate of leaf-wise intersections. We prove that for closed manifolds $M$ whose loop space $\Lambda M$ is "complicated", if $\Sigma \subseteq T^*M$Σ⊆ T*M is a non-degenerate fibrewise starshaped hypersurface and $\varphi \in \mathrm{Ham}_c (T^*M,\omega)$ is a generic Hamiltonian diffeomorphism then the number of leaf-wise intersection points of $\varphi$ in $\Sigma$ grows exponentially in time. Concrete examples of such manifolds are $(S^2 \times S^2)\#(S^2\#S^2)$, $\mathbb{T}^4\#\mathbb{C}P^2$, or any surface of genus greater than one.

Article information

Source
J. Symplectic Geom., Volume 10, Number 4 (2012), 601-653.

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jsg/1357153430

Mathematical Reviews number (MathSciNet)
MR2982024

Zentralblatt MATH identifier
1266.53076

Citation

Macarini, Leonardo; Merry, Will J.; Paternain, Gabriel P. On the growth rate of Leaf-Wise intersections. J. Symplectic Geom. 10 (2012), no. 4, 601--653. https://projecteuclid.org/euclid.jsg/1357153430


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