Research

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).

Career

• 1993-2003 Director, Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, Brazil
• since 1971 Professor, IMPA, Rio de Janeiro, Brazil
• 1968-1971 Scientist, IMPA, Rio de Janeiro, Brazil
• 1967 Ph.D. in Philosophy, University of California (UC) Berkeley, Berkeley, USA
• 1966 M.Sc., University of California Berkeley, Berkeley, USA
• 1962 B.Sc. in Engineering, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

Functions

• 2010-2012 President, Academy of Sciences for the Developing World (TWAS) (today: The World Academy of Sciences)
• 2007-2009 President, TWAS
• 2007-2012 President, Brazilian Academy of Sciences, Brazil
• 2003-2010 Member, Scientific and Strategic Committee, Collège de France (COSS), France
• Coordinator, Study Panel, InterAcademy Partnership (IAP), TWAS
• 2005-2007 Chairperson, Scientific Board, International Centre for Theoretical Physics (ICTP)
• 2000-2006 Secretary General, TWAS and Secretary General, Brazilian Academy of Sciences, Brazil
• 1999-2002 President, Executive Committee, International Mathematical Union (IMU)
• 1995 Scientific Coordinator, Unión Matemática de América Latina y el Caribe (UMALCA)
• 1995 Founder and Chairperson, UMALCA
• 1993-2003 Director, IMPA, Rio de Janeiro, Brazil
• 1993-1996 Chairperson, Scientific Committee, ICTP
• 1993-1996 Vice President and Member, Supervisory Board, International Council for Science (ICS)
• since 1993 Member, Scientific Committee, ICTP
• 1991-1998 Secretary General, Executive Committee, IMU
• since 1990 Member, Scientific Advisory Board, Eidgenössische Technische Hochschule Zürich (ETH Zurich), Zurich, Switzerland
• 1983-1990 Member, Executive Committee, IMU

Projects

• 2010 Project “Non-Uniformly Hyperbolic Horseshoes Arising from Bifurcations of Poincaré Heteroclinic Cycles” (together with Jean-Christophe Yoccoz), Reseau Franco-Brésilien en Mathématiques (GDRI-RFBM) (Brasilian-French Network for Mathematics), France and Brazil
• 2005 Co-Founder, Ramanujan Prize for Young Mathematicians from Developing Countries, International Centre for Theoretical Physics, Trieste, Italy
• 1999-2004 Founding and Board Member, Science Initiative Group, Institute for Advanced Study (IAS), Princeton, USA

Honours and Memberships

• 2013 Solomon Lefschetz Medal, Mathematical Council of the Americas (MCofA)
• since 2010 Member, German National Academy of Sciences Leopoldina, Germany
• 2010 Balzan Prize for Mathematics, Balzan Foundation, Milan, Italy
• 2008 International Prize for Mathematics, Accademia Nazionale dei Lincei, Italy
• since 2006 Member, Russian Academy of Sciences, Russia
• 2006 Trieste Science Prize, Trieste, Italy
• since 2005 Member, Norwegian Academy of Science and Letters (DNVA), Norway
• since 2004 Member, European Academy of Sciences and Arts
• 2000 Premio México de Ciencia y Tecnología, Consejo Nacional de Ciencia y Tecnología (CONACYT), Mexico
• since 1997 Member, Chilean Academy of Sciences, Chile
• since 1996 Member, Indian National Science Academy (INAS), India
• 1995 InterAmerican Prize for Science, Organization of American States (OAS), USA
• since 1992 Member, Latin American Academy of Sciences, Venezuela
• since 1991 Member, World Academy of Sciences (TWAS)
• 1990 Almirante Álvaro Alberto Award, Brazilian National Council for Scientific and Technological Development (CNPq), Brazil
• 1976 Moinho Santista Prize, Brazil
• 1973 Postdoctoral Fellowship, John Simon Guggenheim Memorial Foundation, New York City, USA
• since 1970 Member, Brazilian Academy of Sciences, Brazil
• 1965-1967 Scholarship, National Research Council of Brazil, Brazil
• 1962 Award “Best Graduate”, University of Brazil, Sao Paulo, Brazil