Professor Dr Jacob Palis

Research Priorities: Stability of dynamical systems, bifurcations and fractal dimensions, differential equations, chaotic systems, Morse-Smale diffeomorphisms, metastability, attractors
Jacob Palis is a Brazilian mathematician. He has made significant contributions to the theory of dynamical systems, with which we come into daily contact in the form of markets, nervous systems, societies or ecosystems. He was able to demonstrate that dynamical systems can remain stable and retain their behaviour even under perturbation, which is a discovery of great importance for many areas of science.
Jacob Palis paid particular attention to the stability of dynamical systems, which is closely tied to branches or bifurcations of possible changes. The number of their branches and possible states becomes infinite if one of the parameters changes too much. This means that the dynamical system has become “chaotic” and, as was long assumed, unpredictable. He used an unusual mathematical method to find order in the chaos. He depicted dynamical systems geometrically and was able to demonstrate that chaotic systems, despite the unpredictability of individual events, generally follow certain geometrical rules and repetitive forms, such as doughnuts or curved ribbons. He showed that they can remain stable and retain their “normal” behaviour even in the event of smaller perturbations. This was a groundbreaking discovery. The theory of dynamical systems is now used not only in the fields of cognitive science, climate research, economic sciences and neurosciences but also to analyse models of prebiotic evolution. His theory of “hyperbolic dynamics” and “structural stability” describes virtually all dynamical systems.
In a variety of institutions, Jacob Palis has supported the development of young mathematical talents around the world, particularly in newly industrialised and developing countries. To this end, he developed the Ramanujan Prize for young mathematicians from developing countries (DST-ICTP-IMU Ramanujan Prize) and for several years he held the position of President of the Academy of Sciences for the Developing World (TWAS) today: World Academy of Sciences).