Saghin, Radu

Línea de Investigación

Dynamical Systems, Smooth Ergodic Theory

Publicaciones

• M. Andersson, P. Carrasco and R. Saghin, “Non-uniformly hyperbolic endomorpisms“, Compositio Mathematica, 161 (2025), no. 6, 1313–1356.

• C. Liang, R. Saghin, F. Yang and J. Yang, “Shub’s example revisited“, Ergodic Theory and Dynamical Systems, 45 (2025), no. 3, 894–914.

• R. Saghin, “On invariant holonomies between centers“, Ergodic Theory and Dynamical Systems, 45 (2025), no.1, 274- 293.

• R. Saghin, F. Valenzuela and C. Vasquez, “Differentiability of Lyapunov exponents for diffeomorphisms with dominated splittings“, Memoirs of the American Mathematical Society, volume 300 (2024) , number 1506, 78pp.

• R. Saghin, W. Sun, E. Vargas, “Topological chaos and statistical triviality“, Journal of Mathematical Analysis and Applications, 527 (2023), no. 2, paper no. 127445, 14 pp.

• P. Carrasco, R. Saghin, “Extended flexibility of Lyapunov exponents for Anosov diffeomorphisms“, Transactions of the American mathematical Society, 375, no. 5 (2022), 3411-3449.

• M. Roldan, R. Saghin, J. Yang, “Entropy of partially hyperbolic flows with center dimension two“, Nonlinearity, 33  (2020), no. 2, 790-806.

• R. Saghin, J. Yang, “Lyapunov exponents and rigidity of Anosov automorphisms and skew products“, Advances in Mathematics, 355  (2019), 106764, 45 pp.

• Saghin, R, Yang, J., “Continuity of topological entropy for perturbation of time-one maps of hyperbolic flows”, Israel Journal of Mathematics, 215, 2, 857–875, 2016

• Llibre, J., Saghin, R., Zhang, X., “On the analytic integrability of the 5–dimensional Lorenz system for the gravity–wave activity”, Proceedings of the American Mathematical Society, 142, 2, 531–537, 2014

• Saghin, R., “Volume growth and entropy for C^1 partially hyperbolic diffeomorphisms”, Discrete and Continuous Dynamical Systems – Series A, 34, 9, 3789-3801, 2014

• Saghin, R., Vargas, E., “Invariant measures for Cherry flows”, Communications in Mathematical Physics, 317, 1, 55-67, 2013

• Llibre, J.; Saghin, R. “Topological entropy and periods of graph maps”. J. Difference Equ. Appl. 18 (2012), no. 4, 589–598.

• Llibre, J.; Saghin, R. “The index of singularities of vector fields and finite jets”. J. Differential Equations 251 (2011), no. 10, 2822–2832.

• Saghin, R.; Sun, W.; Vargas, E. “On Dirac physical measures for transitive flows”. Comm. Math. Phys. 298 (2010), no. 3, 741–756.

• Saghin, R.; Xia, Z. “The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center”. Topology Appl. 157 (2010), no. 1, 29–34.

• Llibre, J.; Saghin, R. “Results and open questions on some invariants measuring the dynamical complexity of a map”. Fund. Math. 206 (2009), 307–327.

• Saghin, R. “Note on homology of expanding foliations”. Discrete Contin. Dyn. Syst. Ser. S 2 (2009), no. 2, 349–360.

• Saghin, R.; Xia, Z. “Geometric expansion, Lyapunov exponents and foliations”. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 2, 689–704.

• Hua, Y.; Saghin, R.; Xia, Z. ”Topological entropy and partially hyperbolic diffeomorphisms”. Ergodic Theory Dynam. Systems 28 (2008), no. 3, 843–862.

• Saghin, R. “On the number of ergodic minimizing measures for Lagrangian flows”. Discrete Contin. Dyn. Syst. 17 (2007), no. 3, 501–507 (electronic).

• Saghin, R.; Xia, Z. “Partial hyperbolicity or dense elliptic periodic points for C1-generic symplectic diffeomorphisms”. Trans. Amer. Math. Soc. 358 (2006), no. 11, 5119–5138 (electronic).

• Saghin, R.; Xia, Z. “Generic properties of symplectic diffeomorphisms”. Nonlinear dynamics and evolution equations, 247–255, Fields Inst. Commun., 48, Amer. Math. Soc., Providence, RI, 2006.

Proyectos de Investigación

Externos

• Proyecto MATHAMSUD AMSUD220029, Director del grupo de Chile, 2023-2024.
• Proyecto FONDECYT Regular 1230632, Investigador Responsable, 2023-2027.
• Proyecto MATHAMSUD 21-Math-07, Investigador, 2021-2022.
• Proyecto FONDECYT Postdoctorado 3170049, ” “, Investigador Patrocinante.
• Proyecto de Atracción de Capital Humano Avanzado del Extranjero, MEC, PAI80160049, “Entropía y exponentes de Lyapunov para difeomorfismos parcialmente hiperbólicos”. Investigador Responsable, 2017-2018.
• Proyecto FONDECYT Regular no. 1171477, “Partially hyperbolic systems in low dimensions”. Investigador Responsable, 2017-2021.
• Proyecto MATHAMSUD 16-Math-o6 PHYSECO, Investigador, 2016-2017.
• Proyecto FONDECYT Regular no. 1130611, “Partially hyperbolic and low dimensional dynamics”. Investigador Responsable. 2013-2017.
• Proyecto FONDECYT Anillo “Center of Dynamical Systems and related fields”. Investigador, 2012-2015
• Bolsa regular no pais FAPESP no. 2011/13910-0. “Sistemas Dinâmicos em Dimensões Baixas ou Parcialmente Hyperbólicos”. 2011.
• Marie Curie Intra-European Fellowship No. FP7-IEF-234559. “Smooth Ergodic Theory and partially hyperbolic diffeomorphisms”, 2009-2011.
• Bolsa regular no pais FAPESP no. 2007/03995-2. “Propriedades genéricas de difeomorfismos em dimensões baixas”. 2008-2009

Internos

• Proyecto DI, No. 037.396/2012. “Sistemas Dinámicos en baja dimensión y parcialmente hiperbólicos”. 2012

Conferencias

Some Recent Talks:

• ”Nonuniformly hyperbolic endomorphisms”, Mathematical Congress of the Americas, special session on partially hyperbolic dynamical systems, Miami 2025.

• ”Nonuniformly hyperbolic endomorphisms”, Dynamical Systems Seminar, Université Paris-Saclay, France, February 2025.

• ”Shub’s example revisited“, Workshop 2+3 in Dynamics, UFC, Fortaleza, Brazil, September 2024.

• ”Nonuniformly hyperbolic endomorphisms”, Advances in Dynamics, SUSTech, Shenzhen, China, August 2024.

• ”Shub’s example revisited”, Dynamical Systems Seminar, Peking University, Beijing, China, July 2023.

• ”Lyapunov exponents of hyperbolic and partially hyperbolic diffeomorphisms” Congreso Latino-Americano de Matemáticas, Montevideo, Uruguay (online), September 2021.

• “Regularity of Lyapunov Exponents for Diffeomorphisms with Dominated Splitting“, Dynamical Systems Seminar, Peking University, China, June 2020 (online)

• ”Lyapunov exponents of area preserving endomorphisms”, Workshop on Dynamical Systems and Applications, Universidad de Bio-Bio, Concepción, December 2019.

• ”Regularity of Lyapunov exponents for dominated splittings”, V Escola Brasileira de Sistemas Dinamicos, Belo Horizonte, October 2019.

• ”Regularity of Lyapunov exponents for dominated splittings”, Dynamics Beyond Uniform Hyperbolicity, Marseilles, May 2019.

Dirección de Tesis

Master students:

• Enzo Abraham Fuentes Manriquez, PUCV, 2013.
• Jose Luis Lopez Olate, PUCV, 2018.
• Tadashii Sasaki Horta Salazar, PUCV, 2018 (co-director).
• Bastian Esteban Nuñez Boettiger, PUCV, 2024.
• Francisco Robles Fernandez, PUCV, 2025 (co-director)

PhD Students:

• Enzo Abraham Fuentes Manriquez, PUCV-UTFSM-UV, 2018.
• Bruno Yemini Cabaleiro, PUCV-UTFSM-UV, 2022 (co-director
• Victor Janeiro, UFMG, in progress (co-director)