The height invariant of a four-parameter semitoric system with two focus-focus singularities

Abstract

Semitoric systems are a special class of completely integrable systems with two degrees of freedom that have been symplectically classified by Pelayo and Vu Ngoc about a decade ago in terms of five symplectic invariants. If a semitoric system has several focus-focus singularities, then some of these invariants have multiple components, one for each focus-focus singularity. Their computation is not at all evident, especially in multi-parameter families. In this paper, we consider a four-parameter family of semitoric systems with two focus-focus singularities. In particular, apart from the polygon invariant, we compute the so-called height invariant. Moreover, we show that the two components of this invariant encode the symmetries of the system in an intricate way.

arXiv comment35 pages, 12 figures

References in corpus (6)

• Semitoric integrable systems on symplectic 4-manifolds
• Hamiltonian dynamics and spectral theory for spin-oscillators
• Experimental demonstration of classical Hamiltonian monodromy in the 1:1:2 resonant elastic pendulum
• Taylor series and twisting-index invariants of coupled spin-oscillators
• Fractional bidromy in the vibrational spectrum of HOCl
• Symplectic classification of coupled angular momenta

Cited by in corpus (2)

• Constructions of b-semitoric systems
• The twisting index in semitoric systems