324:"My area of study is measurable dynamics, what is usually called 'ergodic theory'. This is a central branch of dynamical systems with broad connections to smooth and low-dimensional dynamics, symbolic dynamics, topological dynamics, you name it, and to other branches of mathematics, functional analysis, geometry, combinatorics, number theory, you name it. The central assumption of dynamics is that one has a phase space and some group or semigroup of self-maps of that space that play the role of describing time evolution of the phase space."
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773:. In 1991, Mayes choreographed a duet "For Bill and Johnalou", dedicated to Rudolph's parents. In 1991 Rudolph married Michelle Hyde and they had three children, Beatrice, Jonah and Layton. "Rudolph was devoted to his children and evenings became a precious time to be spent with the children - no longer with friends or dance."
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Rudolph was considered dynamic, inspiring and generally positive. For a while he kept a sign in his
Maryland office that read "Eat problems for breakfast". His academic papers were considered difficult to read but in-person he expressed ideas elegantly. His students remembered him as "demanding but
250:, being appointed to the Albert C. Yates Endowed Chair in Mathematics at Colorado State in 2005. He jointly developed a theory of restricted orbit equivalence which unified several other theories. He founded and directed an intense preparation course for graduate math studies and began a
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379:. This is also where he became recognised as a world leader in ergodic theory. He was appointed professor of mathematics in 1985 and was at Maryland until 2004, at which time he was chair of the graduate program and acting chair of the Department of Mathematics.
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and others, entitled "When are two-point extensions of
Bernoulli shifts also Bernoulli shifts?". In so doing he devised the method of "nesting" which evolved into a powerful tool. He also began his studies into varieties of orbit equivalence.
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In
November 1981 Rudolph's older brother Gregory, Gregory's wife Kristin and their two children died in a plane crash. The plane had been piloted by Gregory and had crashed while attempting to land at
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Rudolph was born to
William Franklin Rudolph (1922–2000) and Betty Johnalou Waldner (1921–2004). He was the second of three sons, the others being Gregory and James. The family moved to
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Before he got married, Rudolph had taken dance classes at as a
Caltech undergraduate and at Maryland modern dancing became a serious hobby for him, after being inspired by dance innovator
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As the disease progressed, some physical activities became impossible for
Rudolph, but he continued to teach and do some departmental work, including supervising PhD students. He began a
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for middle school girls with the assistance of a middle school teacher, Martha Cranor. It was later expanded to a summer Math
Circles camp for middle school girls and boys.
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285:, and planned to major in theoretical physics. He soon changed his mind and graduated with a bachelor's degree in mathematics in 1972. Before graduating he won Caltech's
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He founded and directed the SPIRAL program at
Maryland, an intensive six-week preparation for graduate studies in mathematical sciences. It was acknowledged by the
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in 1975, with the thesis "Non-Bernoulli
Behavior of the Roots of K-automorphisms". His work in ergodic theory focused on measure theory, as opposed to the
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for middle-school children. Early in life he was a modern dancer. He died in 2010 from amyotrophic lateral sclerosis, a degenerative motor neuron disease.
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In collaboration with Janet
Kammeyer and others, Rudolph developed a theory of restricted orbit equivalence which unified Ornstein’s Bernoulli theory,
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Rudolph and his family moved to his hometown of Fort Collins in 2005, where he was appointed to the Albert C. Yates Endowed Chair in Mathematics at
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Rudolph, Daniel J.; Schmidt, Klaus (1995). "Almost block independence and bernoullicity of d-actions by automorphisms of compact abelian groups".
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where he was active in the chemistry, physics, computer and flying clubs, and was on the student council. He was a semifinalist in the
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from late 1976 to 1978 and was appointed assistant professor at Stanford University from 1978 to 1981. He spent part of 1979 at the
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Roychowdhury, Mrinal Kanti; Rudolph, Daniel J. (2009). "Any two irreducible Markov chains are finitarily orbit equivalent".
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Rudolph, Daniel J. (December 17, 1997). "Fully generic sequences and a multiple-term return-times theorem".
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865:"Today @ Colorado State University - Daniel J. Rudolph, professor of mathematics, died from ALS Feb. 4"
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He presented several lectures, including one at the 2002 International Congress of Mathematicians in
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In 1981 Rudolph was appointed associate professor at the University of Maryland and was awarded a
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Rudolph died February 4, 2010, from complications from ALS. The April 2012 volume of the journal
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Rudolph, Daniel J. (1976). "Two nonisomorphic K-automorphisms with isomorphic squares".
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Rudolph authored and co-authored more than 70 articles in ergodic theory, including:
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456:(Vol 32, Part 2) was dedicated to him. One of his last papers was a joint work with
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in 1972 where revolutionary work was being done on ergodic theory. He was awarded a
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Daniel J Rudolph in 1972, the year he graduated with B.S. Mathematics from Caltech
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Rudolph was also a visiting professor at several universities, including the
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Boyle, Mike; Weiss, Benjamin (February 7, 2012). "Remembering Dan Rudolph".
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238:. He studied at Caltech and Stanford and taught postgraduate mathematics at
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He graduated from Fort Collins High School in 1968 and matriculated at the
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From August 1975 to August 1976, Rudolph was a postdoctoral fellow at the
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with an award for "Mathematics Programs That Make a Difference" in 2008.
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Fundamentals of measurable dynamics: ergodic theory on Lebesgue spaces
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230:(1949–2010) was a mathematician who was considered a leader in
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Restricted Orbit Equivalence for Actions of Discrete Amenable Groups
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The Lorenz attractor, a visual interpretation of a dynamical system
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364:. At Maryland, he lived at "Ergodic House" with Bruce Kitchens,
749:. Cambridge Tracts in Mathematics. Cambridge University Press.
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Colorado State University memorial page for Daniel J. Rudolph
1083:"The Department of Mathematics at Colorado State University"
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Caltech Mathematics Department prizes and awards (archive)
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Rudolph, Daniel J.; Schwarz, Gideon (1976). "On attaining
559:(3–4). Springer Science and Business Media LLC: 185–190.
491:(3–4). Springer Science and Business Media LLC: 274–287.
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on the conjugacy equivalence relation of automorphisms.
688:(1). Springer Science and Business Media LLC: 349–368.
641:(1). Springer Science and Business Media LLC: 199–228.
596:(1). Springer Science and Business Media LLC: 455–488.
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Non-Bernoulli Behavior of the Roots of K-automorphisms
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Deaths from motor neuron disease in the United States
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Academic staff of the Hebrew University of Jerusalem
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368:and Laif Swanson; they were regularly visited by
828:O'Connor, J.J.; Robertson, E.F. (October 2013).
728:. Oxford science publications. Clarendon Press.
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921:(9). American Mathematical Society (AMS): 1.
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1210:University of Maryland, College Park faculty
915:Notices of the American Mathematical Society
407:University of North Carolina at Chapel Hill
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1170:California Institute of Technology alumni
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397:(1988), the Mathematics Institute of the
415:Université de François Rabelais in Tours
317:approach that dominated ergodic theory.
289:for Undergraduate Mathematics Research.
266:when Daniel was very young. He attended
1180:Neurological disease deaths in Colorado
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403:Nicolaus Copernicus University in Toruń
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743:Kammeyer, J.W.; Rudolph, D.J. (2002).
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1215:21st-century American mathematicians
1165:20th-century American mathematicians
1013:Ergodic Theory and Dynamical Systems
454:Ergodic Theory and Dynamical Systems
320:His description of ergodic theory:
1195:People from Fort Collins, Colorado
279:California Institute of Technology
272:Westinghouse Science Talent Search
14:
1175:Colorado State University faculty
1056:"Browse Prizes and Awards - 2008"
395:Pierre and Marie Curie University
1081:Weston, Nathan (June 10, 2010).
955:Schudel, Matt (March 1, 2010).
911:"Daniel J. Rudolph (1949–2010)"
909:Boyle, Mike (October 1, 2013).
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431:. There he was diagnosed with
330:Hebrew University of Jerusalem
144:Hebrew University of Jerusalem
1:
1130:Mathematics Genealogy Project
1060:American Mathematical Society
863:Warren, Adam (27 July 2010).
681:Israel Journal of Mathematics
552:Israel Journal of Mathematics
484:Israel Journal of Mathematics
440:American Mathematical Society
433:Amyotrophic lateral sclerosis
717:He also authored two books:
1205:Stanford University faculty
281:. He attended Caltech on a
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1200:Stanford University alumni
542:{\displaystyle {\bar {d}}}
411:Université d'Aix-Marseille
348:He became a fellow of the
305:in 1973 and completed his
1107:: CS1 maint: unfit URL (
1026:10.1017/s014338571100112x
694:10.1007/s11856-009-0117-7
429:Colorado State University
377:Sloan Research Fellowship
309:under the supervision of
283:Sloan Research Fellowship
248:Colorado State University
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163:Colorado State University
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972:– via PressReader.
635:Inventiones Mathematicae
590:Inventiones Mathematicae
268:Fort Collins High School
258:Early life and education
722:Rudolph, D.J. (1990).
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372:and Andres del Junco.
358:University of Maryland
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244:University of Maryland
194:Donald Samuel Ornstein
158:University of Maryland
74:Fort Collins, Colorado
16:American mathematician
655:10.1007/s002220050202
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472:Selected publications
466:Annals of Mathematics
399:University of Warwick
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830:"Daniel Jay Rudolph"
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388:Kakutani equivalence
1062:. November 26, 2018
962:The Washington Post
957:"Daniel J. Rudolph"
869:today.colostate.edu
647:1997InMat.131..199R
602:1995InMat.120..455R
315:functional analysis
299:Stanford University
240:Stanford University
94:Stanford University
1126:Daniel Jay Rudolph
1087:math.colostate.edu
784:very supportive".
610:10.1007/bf01241139
565:10.1007/bf02834748
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228:Daniel Jay Rudolph
23:Daniel Jay Rudolph
756:978-0-521-80795-1
735:978-0-19-853572-0
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360:where he studied
303:Master of Science
297:Rudolph moved to
236:dynamical systems
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131:Scientific career
55:Sheridan, Wyoming
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137:Institutions
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1160:2010 deaths
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771:Alvin Mayes
447:Math circle
252:Math circle
1149:Categories
788:References
778:Cedar City
287:Bell Prize
204:Ayşe Şahin
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1042:121494921
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1103:cite web
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417:(1993).
409:(1991),
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122:Children
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622:S2CID
577:S2CID
509:S2CID
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460:and
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