Brazil

Jacob Palis

2010 Balzan Prize for Mathematics (Pure and Applied)

For his fundamental contributions to the mathematical theory of dynamical systems.

The Theory of Dynamical Systems was originated by the great mathematician Henri Poincaré, as a qualitative study of differential equations.For more than forty years, Jacob Palis has made outstanding contributions to this area of Mathematics. Soon after finishing his Ph.D., Jacob Palis became one of the most important contributors to a programme that aimed at describing almost all dynamical systems.In the 1970s following in the wake of Stephen Smale, he was one of the major figures in developing the Theory of Hyperbolic Dynamics and Structural Stability.At the beginning of the 1980s, he initiated, with Newhouse and Takens, what has become one of the most active fields in Dynamics: the interplay between homoclinic or heteroclinic bifurcations and chaos. One of his most important contributions was to reveal, in this context, the fundamental role played by fractal dimensions in connection with the frequency of dynamical bifurcations.Beyond these remarkable achievements, Jacob Palis recently proposed a comprehensive set of conjectures, which together form an ambitious programme to understand the typical behavior of dynamical systems and, in particular, chaotic systems. This programme is currently generating immense scientific activity.Very recently, in conjunction with Jean-Christophe Yoccoz, Jacob Palis has been studying the formation of ‘non-hyperbolic horseshoes’ in the unfolding of homoclinic and heteroclinic tangencies.Not only has Jacob Palis made lasting and influential contributions to Mathematics, but also his record as an advisor is impressive, significantly influencing at least two generations of mathematicians. Thus, he is recognized as the father of the Latin American School of Mathematics in Dynamical Systems and one of the most important scientific personalities on the continent.Jacob Palis has received many international prizes, he is a member of thirteen Academies of Sciences and a holder of honorary degrees from six universities.