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2013
Impact Factor

# Luiz Perona

## Publications:

 Damasceno J. G., Miranda J. A., Perona L. G. A Note on Tonelli Lagrangian Systems on $\mathbb{T}^2$ with Positive Topological Entropy on a High Energy Level 2020, Vol. 16, no. 4, pp.  625-635 Abstract 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. Keywords: Tonelli Lagrangian system, Aubry – Mather theory, static classes Citation: Damasceno J. G., Miranda J. A., Perona L. G.,  A Note on Tonelli Lagrangian Systems on $\mathbb{T}^2$ with Positive Topological Entropy on a High Energy Level, Rus. J. Nonlin. Dyn., 2020, Vol. 16, no. 4, pp.  625-635 DOI:10.20537/nd200407