Resumen de New results in averaging theory and its applications
Murilo Rodolfo Cândido
This work presents new results in the averaging theory for finding periodic solutions. Using Lyapunov-Schmidt reduction and Brouwer's degree we elaborate an averaging theorem able to detect the persistence of periodic solutions in differential systems when the first nonvanishing averaged equation has a continuum of zeros. We also used k-determined hyperbolicity to describe the stability of such periodic solutions. Finally, we use these results to study the periodic solutions of the FitzHugh–Nagumo system, Lorenz system, Maxwell-Bloch system, Noose-Hoover system, Thomas system, Wei system, Wang-Chen system and many others differential systems.
