Period-doubling critical behavior

H - Hamiltonian alphabet

Description The critical situation may appear in two-parameter analysis of generic 2D maps and dissipative systems with 4D phase space as the terminal point of Feigenbaum’s curve. Also it occurs in one-parameter analysis of area-preserving 2D maps, non-autonomous Hamiltonian systems with one degree of freedom, autonomous Hamiltonian systems with 2 degrees of freedom. This type of critical behavior is known after MacKay, Helleman, Eckmann et al. RG equation The fixed-point solution The orbital scaling factors Critical multipliers Relevant eigenvalues Codimension CoDim=2 (restr. 1, for Hamiltonian systems)

Basic model - Hénon map Scaling of the parameter plane with factors Scaling coordinates show enlarged figure Scaling of the phase plane with factors Scaling coordinates show enlarged figure

main science alphabet this page only top