Alphabetical List‎ > ‎P‎ > ‎

Jacob Palis

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


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


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)