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Jorge Lewowicz

Jorge Lewowicz Volman, Uruguayan mathematician (Montevideo 17 March 1937 – Montevideo 21 June 2014)



Obtained a class of topological stable diffeomorphisms wider than the class of Anosov diffeomorphisms

Gave a new proof of stability

With Tolosa showed that expansive homeomorphisms in the Co boundary of Anosov are conjugated

Introduced the concept of persistence in several types of expansive homeomorphisms

Introduced notion of persistence for a homeomorphism of a compact metric space (1983)

Coined the term persistence (1983)

Proved the non existence of stable points in expansive homeomorphisms of surfaces (1983)

Proved that every pseudo-Anosov map is persistent (1983)

Introduced infinitesimal Lyapunov functions or quadratic forms

Proposed  a theorem about expansive homeomorphism of a compact orientable surface (1989) independently of Hiraide (1990)

Proposed the use Lyapunov functions of two variable to study structural stability and similar concepts

Proved, for a differentiable vector or field or a diffeomorphism on a smooth manifold, that the set of points such that the semitrajectories issuing from them approach a particular semitrajectory at a given exponential rate constitute a differentiable submanifold, provided that diferential of the flow has a certain similar behavior on that trajectory (1981)

Gave necessary and sufficient conditions for the existence of an elementary attracting periodic motion of an autonomous system as the only invariant set contained in a given positively invariant region of phase sphere (1974)

With R. Ures proved that if Axiom A diffeomorphisms is exteriorly situated, stable and unstable half-leaves of points of boundedly deviates from geodesics (2000)  

Obtained criteria that assure that certain conservative diffeomorphisms display entropy towards volume    



EPONYMY  

Lewowicz classification of expansive homeomorphism of surfaces

Lewowicz number of linear diffeomorphisms

Lewowicz theorem

Lewowicz map

Lewowicz structural stability theorem

Lewowicz diffeomorphisms