Conjugacy classes and chiral doublets in the Hénon Hamiltonian repeller

Conjugacy classes hidden behind orbital symmetries under reflection are brought to light through the recognition of the fundamental role played by certain algebraic clusters underlying orbital equations of the area-preserving Hénon map, a discrete proxy of open Hamiltonian systems that exhibit chaotic scattering and transport. Specific number-fields ruling orbital coordinates are shown to slave large sets of orbits into being necessarily nonlinearly coupled. Particularly remarkable is the conjugacy class characterized by non-self-symmetric chiral doublets which completely dominates at higher periods.