AbstractThe Collatz Conjecture remains one of the most famous open problems inmathematics. Despite its simple definition, a general proof has yet to be established.In this paper, we propose an approach based on dynamical systems modeling byconstructing an Energy Function with average decay properties, incorporating aLemma based on the results of mathematician Terence Tao. We prove that after afinite number of iterations, the system's energy always decreases, identifying it as aweak Lyapunov function for the Collatz system. This direction opens new possibilitiesin connecting number theory with mathematical physics systems such as entropy,thermodynamics, and discrete dynamics. Keywords: Collatz Conjecture, Lyapunov Function, Dynamical Systems, Number Theory, Energy Decay, Terence Tao.
DO VAN TRUNG (Thu,) studied this question.