Dynamical Systems

Students:

Doctorate:

Eugenio Trucco, Ph. D. advisor at PUC. Thesis "Wandering Fatou components and
algebraic Julia sets" defended on July, 2010. Currently Assistant Professor at Universidad
Austral de Chile, Valdivia.

Master:

Jose David Torres, Master Thesis titled "Tangencias Homoclinicas y Descomposicion
Dominada" defended at PUC, December 2008. Currently he is an instructor (Instructor
Adjunto) at PUC, Santiago.

Manuel Rodrigo Parra, Master Thesis co-advised with Juan Rivera Letelier and titled
"La Medida de Equilibrio de un Endomorsmo Holomorfo de Pk(C)" defended at PUC,
March 2006. In 2011 he obtained a Ph. D. from U. Michigan, Ann Arbor under the
supervision of M. Jonsson.

Gabriela Fernandez, Master Thesis co-advised with Juan Rivera Letelier and titled
"Componentes de Fatou errantes en dinamica polinomial p-adica" defended at PUC, August
2004. In 2011 she obtained her Ph.D. at I.M.P.A., Brazil and currently she is an instructor
(Profesor Asistente Adjunto) at PUC, Santiago.

Undergraduate:

Nicolas Alvarado, Undergraduate Research Experience advisor at PUC, 2015 (Iniciacion
Cientifica). Monograph "El problema del piyama".

Ignacio Barros, Undergraduate Research Experience advisor at PUC, 2011 (Iniciacion
Cientifica). Monograph titled "Teorema de Patchworking y curvas algebraicas planas".
Currently he is a Ph. D. student at the Berlin Mathematical School.

Anibal Medina, Undergraduate Research Experience at PUC, 2008 (Iniciacion Cientifica).
Monograph titled "Algebra conmutativa y variedades afines". Obtained his a Ph. D. Stony Brook University.

Thesis Committee:

Doctorate Gonzalo Castro's Ph. D. Thesis : Probabilistic and Analytical aspects of Nilpotent Group
actions", USACH, April 2013.

Rodrigo Castro's Ph. D. Thesis "Higher order iterative methods on Riemannian manifolds",
USACH, November 2011.

Eduardo Jorquera's Ph. D. Thesis "On group actions on one-dimensional manifolds",
Facultad de Ciencias, U. de Chile, December 2009.

Alvaro Casta~neda's Ph. D. Thesis "Markus-Yamabe Conjecture in Rn and Couples of
Transversal Nets with Singularities", USACH, April 2009.

Gerardo Honorato's Ph. D. Thesis "A dynamical systems approach to root-nding algorithms",
April 2009.

Master Rodrigo Codorniu's Master Thesis "Superficies Fibradas Etale Simplemente Conexas",
PUC, Santiago, June 2014.

Anibal Velozo's Master Thesis "Dinamica en Billares Hiperbolicos", PUC, Santiago, August
2013.

Leslie Jimenez's Master Thesis "Grupos ordenables: estructura algebraica y dinamica",
Facultad de Ciencias, U. de Chile, November 2008.

Romina Menares's Master Thesis : "Billares Duales", Facultad de Ciencias, U. de Chile,
August 2008.

Godofredo Iommi's Master Thesis "Operador de Perron Frobenius y dinamica uno dimensional",
USACH, September 2000.

TALKS:

Title: Irreducibility of periodic curves.

``North-American Workshop in Holomorphic Dynamics, Celebrating John Milnor's 85th. birthday'', Canc\'un, May 31, 2016

``S\'eminaire COOL'', Institut Henri Poincar\'e, Paris, France. April 8, 2016.

Seminar, Ecole Polytechnique, Paris, France. April 5, 2016.

Title: Puiseux series dynamics.

``IV Congress of Latinoamerican Mathematicians'',
Cordoba, Argentina, August 6, 2012.

Title: Puiseux series dynamics and leading monomials of escape regions.

``Workshop on Moduli Spaces Associated to Dynamical Systems'', ICERM, Providence, USA, April 17, 2012.

Title: Rescaling limits of complex rational maps.

``Frontiers in Complex Dynamics'', Banff, Canada, February 24, 2011.

``International Conference on Dynamical Systems'', Buzios, February 25, 2010.

Dynamics Seminar, Toulouse, France, November 26, 2009.

Dynamics Seminar, Liverpool, UK, November 2009.

Title: Iteration of rational maps: for a richer harvest plow on different fields.

Math-Amsud Conference, Lima, Per\'u. November 2008.

Title: Puiseux series dynamics and Quadratic Rational Maps

``First PRIMA Congress'', Sydney, Australia, July 8, 2009.

``Advances in low dimensional dynamics'', Stony Brook, USA, June 9, 2009.

Geometry and Topology Seminar, U. of Illinois, Chicago, USA. November 2008.

Teichmuller Theory Seminar, Marseille, France. June 2008.

Minicourse (3 sessions of 2 hours), CIRM, Luminy, France. June 2008.

Simposio Somachi. August 2007.

Seminario de sistemas din\'amicos UCN, Antofagasta, Chile. March 2007.

Title: Iteration of cubic polynomials and Puiseux series dynamics

``IV Workshop on Dynamical Systems'', San Pedro de Atacama, Chile, August 2005.

``Dynamique conforme, geometrie hyperbolique, et fractions continues'', CIRM, Marseille, France, June 2005.

``Workshop on p-adic dynamics'', Wesleyan, USA, May 2005.

``Workshop on combinatorial methods in complex dynamics'', Warwick, UK, April 2004.

``III Workshop on Dynamical Systems'', San Pedro de Atacama, Chile, August 2003.

Title: Minicourse ``Dynamics in dimension one'' with J. Rivera-Letelier.

Encuentro de la zona sur, Talca, Chile, April 2005.

V Escuela de sistemas dinamicos, Santiago, Chile, January 2005.

Title: On the topology of solenoidal attractors of the cylinder.

``Workshop on combinatorial methods in complex dynamics'', Warwick, UK, April 2004.

``International Congress in Dynamical Systems'', Montevideo, March 2004.

Title: Quadratic polynomials and cubic parameter space.}

``Around Dynamics: A conference in honor of Jack Milnor's seventieth anniversary'', Stony Brook, USA, March 2001.

Title: Real laminations and topological dynamics of complex polynomials

``New Directions in Dynamical Systems'', Kyoto, Japan, August 2002.

``Workshop on Dynamics and Randomness'', Santiago, Chile, December 2000.

In a Session of the ``Regional Meeting'' of the ``American Mathematical Society'', Alabama, USA, November 2000.

Seminario PUC, Lima, Per\'u, October 2000.