jan@mat.ufmg.br

    Публикации:

    , ,
    Подробнее
    In this work we study the dynamical behavior of Tonelli Lagrangian systems defined on the tangent bundle of the torus $\mathbb{T}^2=\mathbb{R}^2/\mathbb{Z}^2$. We prove that the Lagrangian flow restricted to a high energy level $E_{L}^{-1}(c)$ (i.e., $c > c_0(L)$) has positive topological entropy if the flow satisfies the Kupka-Smale property in $E_{L}^{-1}(c)$ (i.e., all closed orbits with energy c are hyperbolic or elliptic and all heteroclinic intersections are transverse on $E_{L}^{-1}(c)$). The proof requires the use of well-known results from Aubry – Mather theory.
    Ключевые слова: Tonelli Lagrangian system, Aubry – Mather theory, static classes
    Цитирование: , , ,  A Note on Tonelli Lagrangian Systems on $\mathbb{T}^2$ with Positive Topological Entropy on a High Energy Level, Нелинейная динамика, 2020, Vol. 16, no. 4, с.  625-635
    DOI:10.20537/nd200407

    Вернуться к списку