New results in averaging theory and its applications
- Autores: Murilo Rodolfo Cândido
- Directores de la Tesis: Jaume Llibre (dir. tes.)
- Lectura: En la Universitat Autònoma de Barcelona ( España ) en 2018
- Idioma: español
- Tribunal Calificador de la Tesis: Joan Torregrosa Arús (presid.) , Isaac García Rodríguez (secret.) , Luís Manuel Gonçalves Barreira (voc.)
- Enlaces
- Resumen
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.
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