Jacob Palis
Encyclopedia
Jacob Palis, Jr. is a Brazil
ian mathematician
and professor
. Since 1973 he has held a permanent position as professor at Instituto Nacional de Matemática Pura e Aplicada in Rio de Janeiro
, Brazil. He was director of the same institute from 1993 until 2003. He was Secretary-General of the Third World Academy of Sciences
from 2004 to 2006, and elected its President in 2006. He was also president of the International Mathematical Union
from 1999 to 2002.
He studied under Stephen Smale
at University of California, Berkeley
, and his 1968 thesis was entitled On Morse-Smale Diffeomorphism
s. Palis himself has advised more than forty Ph.D.
students so far from more than ten countries.
Palis has received numerous medals and decoration. He is a foreign member of several academies of sciences, including the United States National Academy of Sciences
and the French Academy of Sciences
. In 2005 Palis was selected a member of the Legion of Honor.
He is a member of the Norwegian Academy of Science and Letters
. In 2010 he was awarded the Balzan Prize
for his fundamental contributions in the mathematical theory of dynamical systems that has been the basis for many applications in various scientific disciplines (such as in the study of oscillations).
His Erdős number
is 3.
Palis serves on the board of the Science Initiative Group
.
s, attractor
s and chaotic systems.
Books published
Brazil
Brazil , officially the Federative Republic of Brazil , is the largest country in South America. It is the world's fifth largest country, both by geographical area and by population with over 192 million people...
ian mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and professor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
. Since 1973 he has held a permanent position as professor at Instituto Nacional de Matemática Pura e Aplicada in Rio de Janeiro
Rio de Janeiro
Rio de Janeiro , commonly referred to simply as Rio, is the capital city of the State of Rio de Janeiro, the second largest city of Brazil, and the third largest metropolitan area and agglomeration in South America, boasting approximately 6.3 million people within the city proper, making it the 6th...
, Brazil. He was director of the same institute from 1993 until 2003. He was Secretary-General of the Third World Academy of Sciences
Third World Academy of Sciences
TWAS, until 2004 named Third World Academy of Sciences and now TWAS, the academy of sciences for the developing world, is a merit-based science academy uniting 1,000 scientists in some 70 countries. Its principal aim is to promote scientific capacity and excellence for sustainable development in...
from 2004 to 2006, and elected its President in 2006. He was also president of the International Mathematical Union
International Mathematical Union
The International Mathematical Union is an international non-governmental organisation devoted to international cooperation in the field of mathematics across the world. It is a member of the International Council for Science and supports the International Congress of Mathematicians...
from 1999 to 2002.
He studied under Stephen Smale
Stephen Smale
Steven Smale a.k.a. Steve Smale, Stephen Smale is an American mathematician from Flint, Michigan. He was awarded the Fields Medal in 1966, and spent more than three decades on the mathematics faculty of the University of California, Berkeley .-Education and career:He entered the University of...
at University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
, and his 1968 thesis was entitled On Morse-Smale Diffeomorphism
Diffeomorphism
In mathematics, a diffeomorphism is an isomorphism in the category of smooth manifolds. It is an invertible function that maps one differentiable manifold to another, such that both the function and its inverse are smooth.- Definition :...
s. Palis himself has advised more than forty Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
students so far from more than ten countries.
Palis has received numerous medals and decoration. He is a foreign member of several academies of sciences, including the United States National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
and the French Academy of Sciences
French Academy of Sciences
The French Academy of Sciences is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research...
. In 2005 Palis was selected a member of the Legion of Honor.
He is a member of the Norwegian Academy of Science and Letters
Norwegian Academy of Science and Letters
The Norwegian Academy of Science and Letters is a learned society based in Oslo, Norway.-History:The University of Oslo was established in 1811. The idea of a learned society in Christiania surfaced for the first time in 1841. The city of Throndhjem had no university, but had a learned...
. In 2010 he was awarded the Balzan Prize
Balzan Prize
The International Balzan Prize Foundation awards four annual monetary prizes to people or organisations who have made outstanding achievements in the fields of humanities, natural sciences, culture, as well as for endeavours for peace and the brotherhood of man.-Rewards and assets:Each year the...
for his fundamental contributions in the mathematical theory of dynamical systems that has been the basis for many applications in various scientific disciplines (such as in the study of oscillations).
His Erdős number
Erdos number
The Erdős number describes the "collaborative distance" between a person and mathematician Paul Erdős, as measured by authorship of mathematical papers.The same principle has been proposed for other eminent persons in other fields.- Overview :...
is 3.
Palis serves on the board of the Science Initiative Group
Science Initiative Group
The Science Initiative Group is an international team of scientific leaders and supporters dedicated to fostering science in developing countries. SIG was formed to facilitate the Millennium Science Initiative ....
.
Research interests
Palis' research interests are mainly dynamical systems and differential equations. Some themes are: Global stability and hyperbolicity, bifurcationBifurcation
Bifurcation means the splitting of a main body into two parts.Bifurcation or Bifurcated may refer to:*Bifurcation , the division of issues in a trial for example the division of a page into two parts....
s, attractor
Attractor
An attractor is a set towards which a dynamical system evolves over time. That is, points that get close enough to the attractor remain close even if slightly disturbed...
s and chaotic systems.
Selected publications
- On Morse-Smale Dynamical Systems, Topology 19, 1969 (385-405).
- Structural Stability Theorems, with S. SmaleStephen SmaleSteven Smale a.k.a. Steve Smale, Stephen Smale is an American mathematician from Flint, Michigan. He was awarded the Fields Medal in 1966, and spent more than three decades on the mathematics faculty of the University of California, Berkeley .-Education and career:He entered the University of...
, Proceedings of the Institute on Global Analysis, American Math. Society, Vol. XIV, 1970 (223-232). - Cycles and Bifurcations Theory, with S. Newhouse, Asterisque 31, Societe Mathematique de France, 1976 (44-140).
- The Topology of Holomorphic Flows near a Singularity, with C. Camacho and N. KuiperNicolaas KuiperNicolaas Hendrik "Nico" Kuiper was a Dutch mathematician, known for Kuiper's test and proving Kuiper's theorem. He also contributed to the Nash embedding theorem.Kuiper completed his Ph.D...
, Publications Math.Institut Hautes Etudes Scientifiques 48, 1978 (5-38). - Moduli of Stability and Bifurcation Theory, Proceedings of the International Congress of Mathematicians, Helsinki, 1978 (835-839).
- Stability of Parameterized Families of Gradient Vector Fields, with F. TakensFloris TakensFloris Takens was a Dutch mathematician known for contributions to the theory of chaotic dynamical systems.Together with David Ruelle he predicted that fluid turbulence could develop through a strange attractor, a term they coined, as opposed to the then-prevailing theory of accretion of modes....
, Annals of Mathematics 118, 1983 (383-421). - Cycles and Measure of Bifurcation Sets for Two-Dimensional Diffeomorphisms, with F. Takens, Inventiones Mathematicae 82, 1985 (397-422).
- Homoclinic Orbits, Hyperbolic Dynamic and Fractional Dimensions of Cantor Sets (Lefschetz Centennial Conference) Contemporary Mathematics - American Mathematical Society, 58, 1987 (203-216).
- Hyperbolicity and Creation of Homoclinic Orbits, with F.Takens, Annals of Mathematics 125, 1987 (337-374).
- On the C1 Omega-Stability Conjecture, Publications Math. Institut Hautes Etudes Scientifiques, 66, 1988 (210-215).
- Bifurcations and Global Stability of Two-Parameter Families of Gradient Vector Fields with M. J. Carneiro, Publications Math. Institut Hautes Etudes Scientifiques 70, 1990 (103-168).
- Homoclinic Tangencies for Hyperbolic Sets of Large Hausdorff Dimension, with J.C. YoccozJean-Christophe YoccozJean-Christophe Yoccoz is a French mathematician. He was awarded a Fields Medal in 1994, for his work on dynamical systems.-Biography:...
, Acta Mathematica 172, 1994 (91-136). - High Dimension Diffeomorphisms Displaying Infinitely Many Sinks, with M. Viana, Annals of Mathematics 140, 1994 (207 - 250).
- A Global View of Dynamics and a Conjecture on the Denseness of Finitude of Attractors. Astérisque. França: , v.261, p.339 - 351, 2000.
- Homoclinic tangencies and fractal invariants in arbitrary dimension, with C. Moreira and M. Viana, C R Ac Sc Paris., 2001.
- Nonuniformily hyperbolic horseshoes unleashed by homoclinic bifurcations and zero density of attractors, with J.-C. Yoccoz, C R Ac Sc Paris., 2001.
Books published
- Geometric Theory of Dynamical Systems, with W. de Melo. Springer-Verlag, 1982; also published in Portuguese, Russian and Chinese.
- Hyperbolicity and Sensitive-Chaotic Dynamics at Homoclinic Bifurcations, Fractal Dimensions and Infinitely Many Attractors, with F. Takens. Cambridge Univ. Press, 1993; Second Edition, 1994.