Advanced Course on Dynamical Systems [ Back ]

Dates:
01.09.98 - 10.09.98
Place:
Bellaterra, Spain
Organizers:
Lluís Alsedà, Armengol Gasull and Jaume Llibre
Web Site:
http://www.crm.es/Conferences/an...

Participants

T. Barragán, J. Bernat, O.J. Broch, M. Chas, A. Cima, N. Fagella, A. Falcó, C. Inninger, X. Jarque, V. Jiménez, M. Lakner, A.J. López, J.S. Lynch, F. Mañosas, F. Mas, J.M. Moreno, P. Mumbrú, A. Nicolau, P. Petek, J.L. Rodríguez, P. Roesch, A. Sá, M. Seguy, S. Serrano, M. Skapin-Rugelj, C. Stroh, A. Teruel, J.C. Valverde, R. Vigara, J. Villadelprat.

Lessons

  • S. van Strien "Complex dynamics of real polynomials"

    Metric tools in real one-dimensional dynamics. Julia sets and ways of estimating the shape of Yoccoz puzzle pieces. Big moduli in the quadratic case versus small moduli associated to polynomials of higher order. The topology and geometry of Julia sets of real polynomials
  • R. Devaney "Dynamics and topology of entire functions"

    Behavior of entire transcendental functions under iteration. Julia sets and bifurcations sets for such functions. Discussion of the rich topological structures such as Cantor bouquets and Knaster continua associated with these sets. Description in detail of some of the global bifurcations encountered in families of these functions.
  • A. van den Essen "The Jacobian Conjecture and Dynamical Systems"

    Invertible polynomial maps. The Jacobian Conjecture. Stability methods, H(n,A), D(n,A). Linearization conjectures. The Markus-Yamabe conjecture and a conjecture of LaSalle.

Lectures

  • Ll. Alsedà "Dynamics of Hubbard trees"
  • A. Cima "Isochronicity of planar systems and the Jacobian conjecture"
  • N. Fagella "Quasi-conformal surgery on Herman rings of the standard family"
  • Cl. Inninger "Rational functions whose Julia sets are Jordan arcs or curves"
  • X. Jarque "Non regular sequence for complex exponentials. The Misiurewicz case"
  • M. Lakner "The one-equator property"
  • J. Llibre "Periodic orbits for holomorphic maps"
  • J. S. Lynch "The medusa algorithm and polynomial matings"
  • P. Petek "Circles and periodic points in quaternionic Julia sets"
  • P. Roesch "Local connectivity for Newton maps"
  • M. Skapin "The dynamics of l + z + ez"
  • Ch. Stroh "On the connectedness of Julia sets of rational functions"
  • J. C. Valverde "Local bifurcations of one-parameter families of maps under some new non-degenerated conditions"
  • J. Villadelprat "A Poincaré-Hopf theorem for non-compact manifolds"