Rufus Bowen
Encyclopedia
Robert Edward "Rufus" Bowen (23 February 1947 - 30 July 1978) was an internationally known professor in the Department of Mathematics at the University of California, Berkeley
, who specialized in dynamical systems theory
. Bowen's work dealt primarily with axiom A
systems, but the methods he used while exploring topological entropy
, symbolic dynamics
, ergodic theory
, Markov partition
s, and invariant measure
s "have application far beyond the axiom A systems for which they were invented." The Bowen Lectures at the University of California, Berkeley, are given in his honor.
, to Marie DeWinter Bowen, a school teacher, and Emery Bowen, a Travis Air Force Base
budget officer, but he grew up fifteen miles away in Fairfield
, California, where he attended the public schools and graduated from Armijo High School
in 1964. His senior yearbook documents that he played two years of varsity basketball, was a member of the science, math, and language clubs, and was President of the senior class. During his first three years of high school, he finished 102nd, 7th, and 2nd among Californians in the MAA (Mathematical Association of America) mathematics test. In 1964, he finished 2nd in the Westinghouse (now Intel) Science Talent Search
in Washington, D.C. During his senior year in high school, his first published paper appeared in the American Mathematics Monthly.
As an undergraduate at the University of California, Berkeley, Bowen was a Putnam Fellow
in 1964 and 1965. He earned his bachelor's degree from Berkeley where he received, on 15 June 1967, the University Medal as the most distinguished graduating senior. He also received the Dorothea Klumpke Roberts Prize (as top mathematics student) and the Mathematics Department Citation. At this time, Bowen was quoted as saying, "I'm slightly involved in political activity." He was "active in organizations devoted to preventing nuclear war."
Bowen married Carol Twito of Hayward
on 6 March 1968. They had no children.
In 1970, Bowen completed his doctorate in Mathematics at Berkeley under Stephen Smale
, and joined the faculty as assistant professor in that year. At this time he began calling himself Rufus, the nickname he had been given because of his red hair and beard. He was an invited speaker at the 1974 International Mathematical Conference in Vancouver
, British Columbia. He was promoted to full professorship in 1977.
Bowen's mature work dealt with dynamical systems theory, a field which Smale, Bowen's dissertation advisor, explored and broadened in the 1960s.
Bowen was just 31 years old when he died in Santa Rosa
of a cerebral hemorrhage "at the start of what was to have been a vacation trip." Berkeley's Mathematics Department Chairman John L. Kelley
called Bowen a "remarkable, brilliant professor and superb teacher." Dennis Sullivan
wrote, in the issue of Publications mathématiques de l'Institut des hautes études scientifiques dedicated to Bowen's memory,
gave the talks in 2002-3 and Edward Witten
lectured in 2006-7.
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
, who specialized in dynamical systems theory
Dynamical systems theory
Dynamical systems theory is an area of applied mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. When difference...
. Bowen's work dealt primarily with axiom A
Axiom A
In mathematics, Smale's axiom A defines a class of dynamical systems which have been extensively studied and whose dynamics is relatively well understood. A prominent example is the Smale horseshoe map. The term "axiom A" originates with Stephen Smale...
systems, but the methods he used while exploring topological entropy
Topological entropy
In mathematics, the topological entropy of a topological dynamical system is a nonnegative real number that measures the complexity of the system. Topological entropy was first introduced in 1965 by Adler, Konheim and McAndrew. Their definition was modelled after the definition of the...
, symbolic dynamics
Symbolic dynamics
In mathematics, symbolic dynamics is the practice of modeling a topological or smooth dynamical system by a discrete space consisting of infinite sequences of abstract symbols, each of which corresponds to a state of the system, with the dynamics given by the shift operator...
, ergodic theory
Ergodic theory
Ergodic theory is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics....
, Markov partition
Markov partition
A Markov partition is a tool used in dynamical systems theory, allowing the methods of symbolic dynamics to be applied to the study of hyperbolic systems. By using a Markov partition, the system can be made to resemble a discrete-time Markov process, with the long-term dynamical characteristics...
s, and invariant measure
Invariant measure
In mathematics, an invariant measure is a measure that is preserved by some function. Ergodic theory is the study of invariant measures in dynamical systems...
s "have application far beyond the axiom A systems for which they were invented." The Bowen Lectures at the University of California, Berkeley, are given in his honor.
Life
Robert Edward Bowen was born in Vallejo, CaliforniaVallejo, California
Vallejo is the largest city in Solano County, California, United States. The population was 115,942 at the 2010 census. It is located in the San Francisco Bay Area on the northeastern shore of San Pablo Bay...
, to Marie DeWinter Bowen, a school teacher, and Emery Bowen, a Travis Air Force Base
Travis Air Force Base
Travis Air Force Base is a United States Air Force air base under the operational control of the Air Mobility Command , located three miles east of the central business district of Fairfield, in Solano County, California, United States. The base is named for Brigadier General Robert F...
budget officer, but he grew up fifteen miles away in Fairfield
Fairfield, California
Fairfield is a city located in Solano County in Northern California, USA. It is generally considered the midpoint between the cities of San Francisco and Sacramento, approximately from the city center of both cities, approximately from the city center of Oakland, less than from Napa Valley, 18...
, California, where he attended the public schools and graduated from Armijo High School
Armijo High School
Armijo High School is a public secondary school located in Fairfield, California. The school serves about 2500 students in grades 9 to 12 in the Fairfield-Suisun Unified School District....
in 1964. His senior yearbook documents that he played two years of varsity basketball, was a member of the science, math, and language clubs, and was President of the senior class. During his first three years of high school, he finished 102nd, 7th, and 2nd among Californians in the MAA (Mathematical Association of America) mathematics test. In 1964, he finished 2nd in the Westinghouse (now Intel) Science Talent Search
Intel Science Talent Search
The Intel Science Talent Search , known for its first 57 years as the Westinghouse Science Talent Search is a research-based science competition in the United States for high school seniors. It has been referred to as "the nation's oldest and most prestigious" science competition. In his speech...
in Washington, D.C. During his senior year in high school, his first published paper appeared in the American Mathematics Monthly.
As an undergraduate at the University of California, Berkeley, Bowen was a Putnam Fellow
William Lowell Putnam Mathematical Competition
The William Lowell Putnam Mathematical Competition, often abbreviated to the Putnam Competition, is an annual mathematics competition for undergraduate college students of the United States and Canada, awarding scholarships and cash prizes ranging from $250 to $2,500 for the top students and $5,000...
in 1964 and 1965. He earned his bachelor's degree from Berkeley where he received, on 15 June 1967, the University Medal as the most distinguished graduating senior. He also received the Dorothea Klumpke Roberts Prize (as top mathematics student) and the Mathematics Department Citation. At this time, Bowen was quoted as saying, "I'm slightly involved in political activity." He was "active in organizations devoted to preventing nuclear war."
Bowen married Carol Twito of Hayward
Hayward, California
Hayward is a city located in the East Bay in Alameda County, California. With a population of 144,186, Hayward is the sixth largest city in the San Francisco Bay Area and the third largest in Alameda County. Hayward was ranked as the 37th most populous municipality in California. It is included in...
on 6 March 1968. They had no children.
In 1970, Bowen completed his doctorate in Mathematics at Berkeley under Stephen Smale
Stephen Smale
Steven Smale a.k.a. Steve Smale, Stephen Smale is an American mathematician from Flint, Michigan. He was awarded the Fields Medal in 1966, and spent more than three decades on the mathematics faculty of the University of California, Berkeley .-Education and career:He entered the University of...
, and joined the faculty as assistant professor in that year. At this time he began calling himself Rufus, the nickname he had been given because of his red hair and beard. He was an invited speaker at the 1974 International Mathematical Conference in Vancouver
Vancouver
Vancouver is a coastal seaport city on the mainland of British Columbia, Canada. It is the hub of Greater Vancouver, which, with over 2.3 million residents, is the third most populous metropolitan area in the country,...
, British Columbia. He was promoted to full professorship in 1977.
Bowen's mature work dealt with dynamical systems theory, a field which Smale, Bowen's dissertation advisor, explored and broadened in the 1960s.
As studied by Smale, a dynamical system comprises a manifoldManifoldIn mathematics , a manifold is a topological space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold....
and a smooth mapping
:
→
... As Poincaré
Henri PoincaréJules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
emphasized, there is no general procedure for this, and therefore one must resort to describing average, typical, or most probable behavior. Bowen's work is an important part of the program of expressing these vague ideas in mathematically precise and useful ways.
Bowen was just 31 years old when he died in Santa Rosa
Santa Rosa, California
Santa Rosa is the county seat of Sonoma County, California, United States. The 2010 census reported a population of 167,815. Santa Rosa is the largest city in California's Wine Country and fifth largest city in the San Francisco Bay Area, after San Jose, San Francisco, Oakland, and Fremont and 26th...
of a cerebral hemorrhage "at the start of what was to have been a vacation trip." Berkeley's Mathematics Department Chairman John L. Kelley
John L. Kelley
John Leroy Kelley was an American mathematician at University of California, Berkeley who worked in general topology and functional analysis....
called Bowen a "remarkable, brilliant professor and superb teacher." Dennis Sullivan
Dennis Sullivan
Dennis Parnell Sullivan is an American mathematician. He is known for work in topology, both algebraic and geometric, and on dynamical systems. He holds the Albert Einstein Chair at the City University of New York Graduate Center, and is a professor at Stony Brook University.-Work in topology:He...
wrote, in the issue of Publications mathématiques de l'Institut des hautes études scientifiques dedicated to Bowen's memory,
Rufus was special, and I could close with Mike Shub's comment, "Don't forget to say that we all liked him".
Posthumous Honor
Since 1981, an eminent mathematician or scientist has spoken each year under the auspices of The Bowen Lectures at Berkeley. According to the University, "The Bowen Lectures are supported by an anonymous donor, who was an undergraduate student of Rufus Bowen." Most notably, Roger PenroseRoger Penrose
Sir Roger Penrose OM FRS is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College...
gave the talks in 2002-3 and Edward Witten
Edward Witten
Edward Witten is an American theoretical physicist with a focus on mathematical physics who is currently a professor of Mathematical Physics at the Institute for Advanced Study....
lectured in 2006-7.
Selected Published Works
- Bowen: "The sequence
+1 composite for all 
", American Mathematics Monthly, vol. 71 (1964), pp. 175–6. - Bowen: "Topological Entropy and Axiom A" in Global Analysis (Proceedings of Symposia in Pure Mathematics, vol. XIV), American Mathematical Society (Providence, 1970), Shiing-Shen Chern and Stephen Smale, editors, pp. 23–41.
- Bowen: "Markov partitions for Axiom A diffeomorphisms", American Journal of Mathematics, vol. 92 (1970), pp. 725–747.
- Bowen: "Periodic points and measures for Axiom A diffeomorphisms", Transactions of the American Mathematical Society, 1971, pp. 377–397.
- Bowen: "Symbolic Dynamics for Hyperbolic Flows" in Proceedings of the International Congress of Mathematicians (Vancouver, 1974), pp. 299–302.
- Bowen: Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms. (Lecture Notes in Mathematics, no. 470: A. Dold and B. Eckmann, editors). Springer-Verlag (Heidelberg, 1975), 108 pp.
- Bowen and David Ruelle: "The ergodic theory of Axiom A flows", Inventiones Mathematicae, vol. 29 (1975), pp. 181–202.
- Bowen: "Entropy for Maps of the Interval", Topology, vol. 16 (1977); pp. 465–467.
- Bowen: "A Model for Couette Flow-data", in Turbulence Seminar, Proceedings 1976/77 (New York, 1977), P. Bernard and T. Ratin, editors; pp. 117–133.
- Bowen: On Axiom A Diffeomorphisms, (Regional Conference Series in Mathematics, no. 35), Conference Board of the Mathematical Sciences (Providence, 1978), 45 pp. ISBN 0-8218-1685-3.
- Bowen: "Hausdorff Dimension of Quasi-circles", Publications mathématiques de l'Institut des hautes études scientifiques, no. 50 (1979), pp. 11–26.
- Bowen: Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, 2nd Edition, edited by Jean-René Chazottes. Springer-Verlag (Berlin, 2008). ISBN 978-3-540-77605-5.
External links
- Biographical and professional information about Rufus Bowen
- Rufus Bowen at the Mathematics Genealogy Project