The rejection of impredicatively defined mathematical objects (while accepting the natural numbers as classically understood) leads to the position in the philosophy of mathematics known as predicativism, advocated by Henri Poincaré and Hermann Weyl in his Das Kontinuum.
Henri Poincaré proved that the map f is essentially unique: if z0 is an element of U and φ is an arbitrary angle, then there exists precisely one f as above such that f(z0) = 0 and that the argument of the derivative of f at the point z0 is equal to φ.
As Poincaré emphasized, there is no general procedure for this, and therefore one must resort to describing average, typical, or most probable behavior.
Henri Matisse | Henri de la Tour d'Auvergne, Vicomte de Turenne | Bernard-Henri Lévy | Henri Dutilleux | Paul-Henri Mathieu | Henri Poincaré | Robert Henri | Henri Mignet | Henri Cartier-Bresson | Raymond Poincaré | Henri Fayol | Henri Bendel | Henri Barbusse | Jean-Henri Fabre | Henri-Pierre Roché | Henri Langlois | Henri, Grand Duke of Luxembourg | Henri Fantin-Latour | Poincaré sphere | Paul-Henri Spaak | Jacques-Henri Bernardin de Saint-Pierre | Henri Wallon | Henri Vieuxtemps | Henri Vernes | Henri Salvador | Henri Pousseur | Henri Michaux | Henri Guillaumet | Henri Estienne | Poincaré |
The theorem was first studied in view of work on differential equations by the French mathematicians around Poincaré and Picard.
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More than 20 years earlier Henri Poincaré had proved an equivalent result, and 5 years before Brouwer P.
Mathematicians and astronomers (such as Laplace, Lagrange, Gauss, Poincaré, Kolmogorov, Vladimir Arnold, and Jürgen Moser) have searched for evidence for the stability of the planetary motions, and this quest led to many mathematical developments, and several successive 'proofs' of stability for the solar system.
He was awarded a fellowship which enabled him to spend three years on graduate work; one year studying advanced mathematics under Felix Klein at Göttingen, one year studying electricity and mechanics under Ludwig Boltzmann in Vienna, and one year studying under Henri Poincaré in Paris.
Henri Poincaré's 1895 paper Analysis Situs studied three-and-higher-dimensional manifolds(which he called "varieties"), giving rigorous definitions of homology, homotopy (which had originally been defined in the context of late nineteenth-century knot theory, developed by Maxwell and others), and Betti numbers and raised a question, today known as the Poincaré conjecture, based his new concept of the fundamental group.
In the mathematical theory of bifurcations, a Hopf or Poincaré–Andronov–Hopf bifurcation, named after Henri Poincaré, Eberhard Hopf, and Aleksandr Andronov, is a local bifurcation in which a fixed point of a dynamical system loses stability as a pair of complex conjugate eigenvalues of the linearization around the fixed point cross the imaginary axis of the complex plane.