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We present a theoretical analysis of the competition between so-callednuclear Jacobi and Poincar\'e shape transitions in function of spin - at hightemperatures. The latter condition implies the method of choice - a realisticversion of the nuclear Liquid Drop Model (LDM), here: the Lublin-StrasbourgDrop (LSD) model. We address specifically the fact that the Jacobi andPoincar\'e shape transitions are accompanied by the flattening of total nuclearenergy landscape as function of the relevant deformation parameters whatenforces large amplitude oscillation modes that need to be taken into account.For that purpose we introduce an approximate form of the collectiveSchr\"odinger equation whose solutions are used to calculate the most probabledeformations associated with both types of transitions and discuss the physicalconsequences in terms of the associated critical-spin values and transitionsthemselves.

Nuclear Jacobi and Poincar\'e Transitions at High Spins and Temperatures: Account~of~Dynamic~Effects~and~Large-Amplitude Motion