  This report is actually the in-class project of MATH489 FA2022, Dynamics and
Differential Equations in University of Illinois Urbana-Champaign. The report
is mainly about gradient flow of a Morse-type functions (Morse functions,
Morse--Bott functions, etc.) and analytic functions. Several small results that
I develop during the reading are included as well. They have a focus on the
convergence, limiting rate and direction of gradient flow in either setting.
