Jean-Pierre Eckmann

{{Short description|Swiss mathematical physicist (born 1944)}}

{{Use dmy dates|date=October 2020}}

{{Infobox scientist

| name = Jean-Pierre Eckmann

| image = Dold Milnor Salamon Eckmann (cropped).jpg

| image_size = 220

| caption = Eckmann in 2007

| birth_date = {{birth date and age|1944|1|27|df=y}}

| birth_place = Switzerland

| death_date =

| death_place =

| field = Mathematics

| work_institution = University of Geneva

| alma_mater = University of Geneva

| doctoral_advisor = Marcel Guenin

| doctoral_students = {{ubl|Viviane Baladi|Pierre Collet|Martin Hairer}}

| known_for =

| prizes =

| footnotes =

}}

Jean-Pierre Eckmann (born 27 January 1944) is a Swiss mathematical physicist in the department of theoretical physics at the University of Geneva[http://theory.physics.unige.ch/dpt/viewmembers.php Department member listing] {{Webarchive|url=https://web.archive.org/web/20160304034926/http://theory.physics.unige.ch/dpt/viewmembers.php |date=4 March 2016 }}, Theoretical Physics, University of Geneva, retrieved 2011-04-29. and a pioneer of chaos theory and social network analysis.{{citation|title=Bursts: the hidden pattern behind everything we do|first=Albert-László|last=Barabási|authorlink=Albert-László Barabási|publisher=Penguin|year=2010|isbn=978-0-525-95160-5|url=https://books.google.com/books?id=ZfqVp2cMODkC&pg=PT87|page=87}}.

Eckmann is the son of mathematician Beno Eckmann.[http://www.geni.com/people/Jean-Pierre-Eckmann/6000000005004900978 Profile for Jean-Pierre Eckmann on geni.com], retrieved 2011-04-30; [http://owpdb.mfo.de/detail?photo_id=11922 Photo of Jean-Pierre Eckmann as a child] with his parents, in the mathematical photo collection of the Mathematical Research Institute of Oberwolfach, retrieved 2011-04-30. He completed his PhD in 1970 under the supervision of Marcel Guenin at the University of Geneva.{{mathgenealogy|id=29332}} He has been a member of the Academia Europaea since 2001.[http://www.ae-info.org/ae/User/Eckmann_Jean-Pierre Academy of Europe: Eckmann Jean-Pierre], retrieved 2011-04-29; {{citation|url=http://www.acadeuro.org/fileadmin/user_upload/files_prev_site/tree17.pdf |contribution=New members of the Academia Europaea admitted 2001 |page=13 |date=January 2002 |volume=17 |title=The Tree: Newsletter of Academia Europaea |url-status=dead |archive-url=https://web.archive.org/web/20110809082542/http://www.acadeuro.org/fileadmin/user_upload/files_prev_site/tree17.pdf |archive-date= 9 August 2011 }}. In 2012, he became a fellow of the American Mathematical Society.[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2012-11-10. He is also a member of the Göttingen Academy of Sciences and Humanities.{{Cite web|url=https://adw-goe.de/en/mitglieder/|title=Members: Göttingen Academy of Sciences and Humanities (AdW)|website=adw-goe.de|access-date=2018-09-04}}

With Pierre Collet and Oscar Lanford, Eckmann was the first to find a rigorous mathematical argument for the universality of period-doubling bifurcations in dynamical systems, with scaling ratio given by the Feigenbaum constants.{{citation|title=Metamagical themas: questing for the essence of mind and pattern|first=Douglas R.|last=Hofstadter|authorlink=Douglas Hofstadter|publisher=Basic Books|year=1996|isbn=978-0-465-04566-2|pages=382–383|url=https://books.google.com/books?id=o8jzWF7rD6oC&pg=PA382}}; {{citation|page=189|title=Does God play dice?: the new mathematics of chaos|first=Ian|last=Stewart|authorlink=Ian Stewart (mathematician)|edition=2nd|publisher=Wiley-Blackwell|year=2002|isbn=978-0-631-23251-3}}. In a highly cited 1985 review paper with David Ruelle,{{citation

| last1 = Eckmann | first1 = J.-P.

| last2 = Ruelle | first2 = D. | author2-link = David Ruelle

| doi = 10.1103/RevModPhys.57.617

| mr = 800052

| issue = 3, part 1

| journal = Reviews of Modern Physics

| pages = 617–656

| title = Ergodic theory of chaos and strange attractors

| volume = 57

| year = 1985|bibcode = 1985RvMP...57..617E }}. he bridged the contributions of mathematicians and physicists to dynamical systems theory and ergodic theory,Review of {{harvtxt|Eckmann|Ruelle|1985}} by Charles Tresser in Mathematical Reviews, {{MR|800052}}. put the varied work on dimension-like notions in these fields on a firm mathematical footing,Review of {{harvtxt|Barreira|Pesin|Schmeling|1999}} by Boris Hasselblatt in Mathematical Reviews, {{MR|1709302}}. and formulated the Eckmann–Ruelle conjecture on the dimension of hyperbolic ergodic measures, "one of the main problems in the interface of dimension theory and dynamical systems".{{citation|title=Dimension theory in dynamical systems: contemporary views and applications|series=Chicago lectures in mathematics|first=Yakov B.|last=Pesin|publisher=University of Chicago Press|year=1997|isbn=978-0-226-66221-3|page=270|url=https://books.google.com/books?id=8h1u9vsTfMkC&pg=PA270}}. A proof of the conjecture was finally published 14 years later, in 1999.{{citation

| last1 = Barreira | first1 = Luis

| last2 = Pesin | first2 = Yakov

| last3 = Schmeling | first3 = Jörg

| doi = 10.2307/121072

| mr = 1709302

| issue = 3

| journal = Annals of Mathematics | series = 2nd ser.

| pages = 755–783

| title = Dimension and product structure of hyperbolic measures

| volume = 149

| year = 1999| jstor = 121072

| arxiv = math/9905205| bibcode = 1999math......5205B

| s2cid = 5973689

}}. Eckmann has done additional mathematical work in very diverse fields such as statistical mechanics, partial differential equations, and graph theory.

His PhD students have included Viviane Baladi, Pierre Collet, and Martin Hairer.