. . . . . . . . "John Norman Mather (* 9. Juni 1942 in Los Angeles, Kalifornien; \u2020 28. Januar 2017 in Princeton, New Jersey) war ein US-amerikanischer Mathematiker, der sich mit Differentialtopologie besch\u00E4ftigte, speziell der Singularit\u00E4tentheorie (\u201EKatastrophentheorie\u201C)."@de . . "Smooth functions"@en . . "John Norman Mather (* 9. Juni 1942 in Los Angeles, Kalifornien; \u2020 28. Januar 2017 in Princeton, New Jersey) war ein US-amerikanischer Mathematiker, der sich mit Differentialtopologie besch\u00E4ftigte, speziell der Singularit\u00E4tentheorie (\u201EKatastrophentheorie\u201C)."@de . . . . . . "\u062C\u0648\u0646 \u0645\u0627\u062B\u0631 (\u0631\u064A\u0627\u0636\u064A\u0627\u062A\u064A)"@ar . . "United States"@en . . . . . . . . . . . . . "1058454905"^^ . . . . . "American"@en . . . . "2017-01-28"^^ . . . . "\u0414\u0436\u043E\u043D \u041D\u043E\u0440\u043C\u0430\u043D \u041C\u0430\u0301\u0437\u0435\u0440 (\u0430\u043D\u0433\u043B. John Norman Mather; 9 \u0438\u044E\u043D\u044F 1942, \u041B\u043E\u0441-\u0410\u043D\u0434\u0436\u0435\u043B\u0435\u0441, \u0421\u0428\u0410 \u2014 28 \u044F\u043D\u0432\u0430\u0440\u044F 2017, \u041F\u0440\u0438\u043D\u0441\u0442\u043E\u043D, \u041D\u044C\u044E-\u0414\u0436\u0435\u0440\u0441\u0438, \u0421\u0428\u0410) \u2014 \u0430\u043C\u0435\u0440\u0438\u043A\u0430\u043D\u0441\u043A\u0438\u0439 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A, \u0441\u043F\u0435\u0446\u0438\u0430\u043B\u0438\u0441\u0442 \u0432 \u043E\u0431\u043B\u0430\u0441\u0442\u0438 \u0442\u0435\u043E\u0440\u0438\u0438 \u043E\u0441\u043E\u0431\u0435\u043D\u043D\u043E\u0441\u0442\u0435\u0439 \u0433\u043B\u0430\u0434\u043A\u0438\u0445 \u043E\u0442\u043E\u0431\u0440\u0430\u0436\u0435\u043D\u0438\u0439 \u0438 \u0442\u0435\u043E\u0440\u0438\u0438 \u0434\u0438\u043D\u0430\u043C\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043C (\u0432 \u0447\u0430\u0441\u0442\u043D\u043E\u0441\u0442\u0438, \u0433\u0430\u043C\u0438\u043B\u044C\u0442\u043E\u043D\u043E\u0432\u043E\u0439 \u043C\u0435\u0445\u0430\u043D\u0438\u043A\u0435)."@ru . "8992"^^ . . . . "\u0414\u0436\u043E\u043D \u041D\u043E\u0440\u043C\u0430\u043D \u041C\u0430\u0301\u0437\u0435\u0440 (\u0430\u043D\u0433\u043B. John Norman Mather; 9 \u0438\u044E\u043D\u044F 1942, \u041B\u043E\u0441-\u0410\u043D\u0434\u0436\u0435\u043B\u0435\u0441, \u0421\u0428\u0410 \u2014 28 \u044F\u043D\u0432\u0430\u0440\u044F 2017, \u041F\u0440\u0438\u043D\u0441\u0442\u043E\u043D, \u041D\u044C\u044E-\u0414\u0436\u0435\u0440\u0441\u0438, \u0421\u0428\u0410) \u2014 \u0430\u043C\u0435\u0440\u0438\u043A\u0430\u043D\u0441\u043A\u0438\u0439 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A, \u0441\u043F\u0435\u0446\u0438\u0430\u043B\u0438\u0441\u0442 \u0432 \u043E\u0431\u043B\u0430\u0441\u0442\u0438 \u0442\u0435\u043E\u0440\u0438\u0438 \u043E\u0441\u043E\u0431\u0435\u043D\u043D\u043E\u0441\u0442\u0435\u0439 \u0433\u043B\u0430\u0434\u043A\u0438\u0445 \u043E\u0442\u043E\u0431\u0440\u0430\u0436\u0435\u043D\u0438\u0439 \u0438 \u0442\u0435\u043E\u0440\u0438\u0438 \u0434\u0438\u043D\u0430\u043C\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043C (\u0432 \u0447\u0430\u0441\u0442\u043D\u043E\u0441\u0442\u0438, \u0433\u0430\u043C\u0438\u043B\u044C\u0442\u043E\u043D\u043E\u0432\u043E\u0439 \u043C\u0435\u0445\u0430\u043D\u0438\u043A\u0435)."@ru . "John Mather (Mathematiker)"@de . . . . . . "John Norman Mather (June 9, 1942 \u2013 January 28, 2017) was a mathematician at Princeton University known for his work on singularity theory and Hamiltonian dynamics. He was descended from Atherton Mather (1663\u20131734), a cousin of Cotton Mather. His early work dealt with the stability of smooth mappings between smooth manifolds of dimensions n (for the source manifold N) and p (for the target manifold P). He determined the precise dimensions (n,p) for which smooth mappings are stable with respect to smooth equivalence by diffeomorphisms of the source and target (i.e., infinitely differentiable coordinate changes)."@en . . . . "1343987"^^ . . . . . . . . . . . . . . . . . . "John Mather (matem\u00E1tico)"@pt . . . . . "\u062C\u0648\u0646 \u0645\u0627\u062B\u0631 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: John N. Mather)\u200F (\u0648. 1942 \u2013 2017 \u0645) \u0647\u0648 \u0631\u064A\u0627\u0636\u064A\u0627\u062A\u064A\u060C \u0648\u0623\u0633\u062A\u0627\u0630 \u062C\u0627\u0645\u0639\u064A \u0623\u0645\u0631\u064A\u0643\u064A\u060C \u0648\u0644\u062F \u0641\u064A \u0644\u0648\u0633 \u0623\u0646\u062C\u0644\u0648\u0633\u060C \u0643\u0627\u0646 \u0639\u0636\u0648\u064B\u0627 \u0641\u064A \u0627\u0644\u0623\u0643\u0627\u062F\u064A\u0645\u064A\u0629 \u0627\u0644\u0648\u0637\u0646\u064A\u0629 \u0644\u0644\u0639\u0644\u0648\u0645\u060C \u062A\u0648\u0641\u064A \u0641\u064A \u0628\u0631\u064A\u0646\u0633\u062A\u0648\u0646\u060C \u0639\u0646 \u0639\u0645\u0631 \u064A\u0646\u0627\u0647\u0632 75 \u0639\u0627\u0645\u0627\u064B."@ar . . "\u062C\u0648\u0646 \u0645\u0627\u062B\u0631 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: John N. Mather)\u200F (\u0648. 1942 \u2013 2017 \u0645) \u0647\u0648 \u0631\u064A\u0627\u0636\u064A\u0627\u062A\u064A\u060C \u0648\u0623\u0633\u062A\u0627\u0630 \u062C\u0627\u0645\u0639\u064A \u0623\u0645\u0631\u064A\u0643\u064A\u060C \u0648\u0644\u062F \u0641\u064A \u0644\u0648\u0633 \u0623\u0646\u062C\u0644\u0648\u0633\u060C \u0643\u0627\u0646 \u0639\u0636\u0648\u064B\u0627 \u0641\u064A \u0627\u0644\u0623\u0643\u0627\u062F\u064A\u0645\u064A\u0629 \u0627\u0644\u0648\u0637\u0646\u064A\u0629 \u0644\u0644\u0639\u0644\u0648\u0645\u060C \u062A\u0648\u0641\u064A \u0641\u064A \u0628\u0631\u064A\u0646\u0633\u062A\u0648\u0646\u060C \u0639\u0646 \u0639\u0645\u0631 \u064A\u0646\u0627\u0647\u0632 75 \u0639\u0627\u0645\u0627\u064B."@ar . . . . "John N. Mather"@fr . . . . . . . . . . . . . "John Norman Mather (June 9, 1942 \u2013 January 28, 2017) was a mathematician at Princeton University known for his work on singularity theory and Hamiltonian dynamics. He was descended from Atherton Mather (1663\u20131734), a cousin of Cotton Mather. His early work dealt with the stability of smooth mappings between smooth manifolds of dimensions n (for the source manifold N) and p (for the target manifold P). He determined the precise dimensions (n,p) for which smooth mappings are stable with respect to smooth equivalence by diffeomorphisms of the source and target (i.e., infinitely differentiable coordinate changes). Mather also proved the conjecture of the French topologist Ren\u00E9 Thom that under topological equivalence smooth mappings are generically stable: the subset of the space of smooth mappings between two smooth manifolds consisting of the topologically stable mappings is a dense subset in the smooth Whitney topology. His notes on the topic of topological stability are still a standard reference on the topic of topologically stratified spaces. In the 1970s, Mather switched to the field of dynamical systems. He made the following main contributions to dynamical systems that deeply influenced the field. 1. He introduced the concept of and gave a characterization of Anosov diffeomorphisms. 2. Jointly with Richard McGehee, he gave an example of collinear four-body problem which has initial conditions leading to solutions that blow up in finite time. This was the first result that made the Painlev\u00E9 conjecture plausible. 3. He developed a variational theory for the globally action minimizing orbits for twist maps (convex Hamiltonian systems of two degrees of freedom), along the line of the work of George David Birkhoff, Marston Morse, Gustav A. Hedlund, et al. This theory is now known as . 4. He developed the Aubry\u2013Mather theory in higher dimensions, a theory which is now called . This theory turned out to be deeply related to the viscosity solution theory of Michael G. Crandall, Pierre-Louis Lions et al. for Hamilton\u2013Jacobi equation. The link was revealed in the of Albert Fathi. 5. He announced a proof of Arnold diffusion for nearly integrable Hamiltonian systems with three degrees of freedom. He prepared the technique, formulated a proper concept of genericity and made some important progresses towards its solution. 6. In a series of papers, he proved that for certain regularity r, depending on the dimension of the smooth manifold M, the group Diff(M, r) is perfect, i.e. equal to its own commutator subgroup, where Diff(M, r) is the group of C^r diffeomorphisms of a smooth manifold M that are isotopic to the identity through a compactly supported C^r isotopy. He also constructed counterexamples where the regularity-dimension condition is violated. Mather was one of the three editors of the Annals of Mathematics Studies series published by Princeton University Press. He was a member of the National Academy of Sciences beginning in 1988. He received the John J. Carty Award of the National Academy of Sciences in 1978 (for pure mathematics) and the George David Birkhoff Prize in applied mathematics in 2003. He also received the Brazilian Order of Scientific Merit in 2000 and the Brouwer Medal from the Royal Dutch Mathematical Society in 2014."@en . . . "John Norman Mather (Los Angeles, 9 de junho de 1942 \u2013 Princeton, 28 de janeiro de 2017) foi um matem\u00E1tico estadunidense conhecido por seu trabalho em teoria das singularidades e mec\u00E2nica hamiltoniana. Foi palestrante convidado do Congresso Internacional de Matem\u00E1ticos em Vancouver (1974: Foliations and local homology groups of diffeomorphisms) e em Berkeley (1986: Dynamics of area preserving mappings)."@pt . . . . . . . . . . . "\u041C\u0430\u0437\u0435\u0440, \u0414\u0436\u043E\u043D \u041D\u043E\u0440\u043C\u0430\u043D"@ru . . . . . . "1942-06-09"^^ . . . . "2017-01-28"^^ . . . . . . . . . . . "John Norman Mather"@en . "1942-06-09"^^ . "John Norman Mather (Los Angeles, 9 de junho de 1942 \u2013 Princeton, 28 de janeiro de 2017) foi um matem\u00E1tico estadunidense conhecido por seu trabalho em teoria das singularidades e mec\u00E2nica hamiltoniana. Foi palestrante convidado do Congresso Internacional de Matem\u00E1ticos em Vancouver (1974: Foliations and local homology groups of diffeomorphisms) e em Berkeley (1986: Dynamics of area preserving mappings)."@pt . . "John N. Mather"@en . . . . . . . . . . . . . . "Mather at Oberwolfach in 2005"@en . . . "John Norman Mather (9 juin 1942 - 28 janvier 2017) est un math\u00E9maticien de l'Universit\u00E9 de Princeton connu pour ses travaux sur la th\u00E9orie de la singularit\u00E9 et la dynamique hamiltonienne."@fr . . . . . . . . . . . . "John Norman Mather (9 juin 1942 - 28 janvier 2017) est un math\u00E9maticien de l'Universit\u00E9 de Princeton connu pour ses travaux sur la th\u00E9orie de la singularit\u00E9 et la dynamique hamiltonienne."@fr . . . . . . . . . . . . . . "Princeton University"@en . . . . . . . . "John Norman Mather"@en . . . . . . . .