Multiplicity of Brake Orbits on a Fixed Energy Surface

Chungen Liu
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Chungen Liu: Guangzhou University, School of Mathematical and Information Science

Chapter Chapter 10 in Index theory in nonlinear analysis, 2019, pp 275-291 from Springer

Abstract: Abstract For the standard symplectic space (R 2n, ω 0) with ω 0(x, y) = 〈Jx, y〉, where J = 0 − I I 0 $$J=\left (\begin {array}{cc}0&-I\\mathrm{i}&0\\\end {array}\right )$$ is the standard symplectic matrix and I is the n × n identity matrix, an involution matrix defined by N = − I 0 0 I $$N=\left (\begin {array}{cc}-I&0\\0&I\end {array}\right )$$ is clearly anti-symplectic, i.e., NJ = −JN. The fixed point set of N and − N are the Lagrangian subspaces L 0 = {0}×R n and L 1 = R n ×{0} of (R 2n, ω 0) respectively.

Date: 2019
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DOI: 10.1007/978-981-13-7287-2_10

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