Biography
Jacob Palis Jr., Brazilian mathematician (Uberaba, Minas Gerais State 15 March 1940 –
From Greek-Lebanese father and Syrian mother
Authored over 80 papers
Respected as one of founders of modern theory of dynamical systems and one of world’s foremost in field of multivariable dynamic systems
First to prove mathematical stable systems occur in any configuration space
Proved that gradient-like dynamical systems in lower dimensions are stable providing the first class of stable systems existing on any smooth configuration space
Established the opening and structure stability of Morse-Smale systems
Demonstrated the existence of structurally stable dynamics systems in all 3-dimension compact varieties
Demonstrated the existence of dynamical cycles in non-wandering sets of dynamic systems
Demonstrated the tubular families technique
Showed that homoclinic bifurcations gave birth to a variety of dynamics complex changes and formulated a series of conjectures proposing that such mechanisms occur in global instabilities of dynamics
Suggested that homoclinic bifurcations are a main mechanism for the nonhiperbolicity of a system
Formulated a series of conjectures in which homoclinic bifurcations are the key mechanism underlying global instabilities of the dynamical behavior
Formulated a series of conjectures describing the orbiting behavior of most typical systems
With M. Viana introduced the notion of intrinsic differentiability and showed continuity of the Hausdorff dimension in the surfaces
Proved C1-stability conjecture (1987)
With J.C. Yoccoz proposed a theorem on the triviality of centralizers of diffeomorphisms and proved that the majority of centralizers for hyperbolic dynamical systems admit only trivial smooth symmetries
Revealed the fundamental role played by fractal dimensions in connection with the frequency of dynamical bifurcations
Formulated a conjecture relating the structure of the arithmetic difference of fractal sets to their fractal dimensions (solved by Moreira and Yoccoz)
Introduced the use of certain smooth invariants for topological equivalence of dynamical systems
With F. Takens proved that most parametrized families of gradient-like vector fields are stable
Created the notion of stable foliations
EPONYMY
Palis conjecture (1980s)
Palis-Smale theorem
Palis-Smale stability conjectures
Malta-Palis theorem
Palis lambda lemma
Hirsch-Palis-Pugh-Shub theorem
Palis invariant
Palis program
HONOURS
Invited Speaker, International Congress of Mathematics, Helsinki (1978)
President, International Mathematical Union (1999-2002)
Associate Foreign Member, National Academy of Sciences (2001) & Academie Française des Sciences (2002)
International Prize in Mathematics, Academia Nazionale dei Lincei (2008)
Balzan Prize for Mathematics (2010)
Solomon Lefschetz Medal, Mathematical Congress of the Americas (2013)
