Different types of critical behavior in conservatively coupled Hénon maps

We study the dynamics of two conservatively coupled H\'enon maps at different levels of dissipation. It is shown that the decrease of dissipation leads to changes in the structure of the parameter plane and the scenarios of transition to chaos compared to the case of infinitely strong dissipation. Particularly, the Feigenbaum line becomes divided into several fragments. Some of these fragments have critical points of different types, namely, of C and H type, as their terminal points. Also the mechanisms of formation of these Feigenbaum line ruptures are described.