Saghin, Radu

Línea de Investigación

Sistemas Dinámicos

Publicaciones

• 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 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 Asociado, 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 Asociado. 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

• “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.
• ”Exponentes de Lyapunov y rigidez para difeomorfismos hiperbólicos y parcialmente hiperbólicos”, Seminario de Sistemas Dinámicos de Santiago, PUC, October 2018.
• ”Lyapunov exponents and rigidity for hyperbolic and partially hyperbolic diffeomorphisms”, International Conference on Dynamical Systems, SUSTech, Shenzhen, June 2018.
• ”Rigidez en Sistemas Dinámicos”, Seminario ”Cruz del Sur”, Universidad de la Frontera, Temuco, May 2018.
• ”Introduction to the dynamics of the quadratic family”, mini-course at Summer School in Mathematics, Universidade Federal de Santa Catarina – Florianopolis, February 2018.
• ”Regularity of integrated Lyapunov exponents II: General results for dominated splittings”, MathamSud Meeting ”PHYSECO”, Montevideo, December 2017.
• “Diferenciabilidad de exponentes de Lyapunov”, XXVI Congreso de Matemática Capricornio, Arica, August 2017.
• ”Invariant measures for Cherry flows”, International Conference on Statistical Properties of Nonequilibrium Dynamical Systems, SUSTC Shenzhen, China, July-August 2016.
• ”Entropy for partially hyperbolic systems with low dimensional center”, School on Algebraic, Geometric and Probabilistic Aspects of Dynamical Systems and Control Theory, ICTP Trieste, Italy, July 2016.
• ”Partially hyperbolic diffeomorphisms with 1-dimensional center”, Valparaiso’s dynamics working days: Groups and low dimensional dynamics, October 2015.
• ”Foliaciones invariantes para los difeomorfismos de Anosov”, Coloquio de Matemáticas, Universidad de Chile, Santiago, June 2015
• “Continuidad de la entropía topológica para difeomorfismos parcialmente hiperbólicos”, ”Dinamica del Norte” Seminar, Universidad Católica del Norte, Antofagasta, June 2015
• ”Continuity of topological entropy for partially hyperbolic diffeomorphisms”, AIMS International Conference on Dynamical Systems, Differential Equations and Applications, Madrid, July 2014
• “Continuity of topological entropy for partially hyperbolic diffeomorphisms“, charla subplenaria  LXXXII Encuentro Anual SOMACHI, November 2013.
• “Volume growth and entropy for PHD’s“. Dynamical Systems Seminar, UFF, Niteroi, Brazil. September, 2013.
• “Volume growth and entropy for partially hyperbolic diffeomorfisms“. Congreso Montevideo Dynamical Systems Conference 2012. Universidad de la República, Uruguay. 13 al 17 de agosto, 2012.
• “Invariant measures for flows on surfaces”. LXI Coloquio de Sistemas Dinámicos, Valdivia, Chile. October, 2012.
• “Volume growth and entropy for partially hyperbolic diffeomorphisms”. Dynamical Systems Seminar, USACH, Santiago, Chile. May, 2012.
• ”Index of singularities of vector field and finite jets”. Dynamical Systems Seminar, UAB Barcelona, Spain. June, 2011.
• ”The index of singularities of vector fields and finite jets”. Dynamical Systems Seminar, IME-USP Sao Paulo, Brazil. March, 2011.
• ”Integrability of invariant distributions”. UB-UPC Dynamical Systems Seminar, UPC, Barcelona, Spain. February, 2011.
• ”On the index of singularities of vector fields”. Analysis Seminar, De Paul University, Chicago, USA. November, 2010.
• ”Dirac physical measures for transitive flows”. AIMS Conference on Dynamical Systems, Differential Equations and Applications, Dresden, Germany. May, 2010.
• ”On physical measures for flows on surfaces”. EDAI Seminar, UFF/UFRJ/PUC, Rio de Janeiro, Brazil. June, 2009.
• ”Volume growth of expanding foliations and applications to entropy” and ”Some examples of physical measures for transitive systems”. Dynamics Days, ICMC USP Sao Carlos, Brazil. March, 2009.
• ”The entropy conjecture for partially hyperbolic diffeomorphisms with 1-d center”. Workshop de Topología e Dinámica, UFF, Niteroi, Brazil. February, 2009.
• ”Introduction to Partially Hyperbolic Diffeomorphisms”. Mini-course, IME-USP Sao Paulo, Brazil. October/November, 2009.

Dirección de Tesis

Magister

Enzo Fuentes. “Medidas invariantes y operadores de transferencia para algunos sistemas dinámicos”. Finalizado. Magíster en Matemáticas, Pontificia Universidad Católica de Valparaíso. 2013.