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Anatole Katok
Anatoly Borisovich Katok (russian: Анатолий Борисович Каток; August 9, 1944 – April 30, 2018) was an American mathematician with Russian-Jewish origins. Katok was the director of the Center for Dynamics and Geometry at the Pennsylvania State University. His field of research was the theory of dynamical systems. Early life and education Anatole Katok graduated from Moscow State University, from which he received his master's degree in 1965 and PhD in 1968 (with a thesis on "Applications of the Method of Approximation of Dynamical Systems by Periodic Transformations to Ergodic Theory" under Yakov Sinai). In 1978 he immigrated to the USA. He was married to the mathematician Svetlana Katok, who also works on dynamical systems and has been involved with Katok in the MASS Program for undergraduate students at Penn State. Work and research While in graduate school, Katok (together with A. Stepin) developed a theory of periodic approximations of measure-pre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Washington, D
Washington commonly refers to: * Washington (state), United States * Washington, D.C., the capital of the United States ** A metonym for the federal government of the United States ** Washington metropolitan area, the metropolitan area centered on Washington, D.C. * George Washington (1732–1799), the first president of the United States Washington may also refer to: Places England * Washington, Tyne and Wear, a town in the City of Sunderland metropolitan borough ** Washington Old Hall, ancestral home of the family of George Washington * Washington, West Sussex, a village and civil parish Greenland * Cape Washington, Greenland * Washington Land Philippines *New Washington, Aklan, a municipality *Washington, a barangay in Catarman, Northern Samar *Washington, a barangay in Escalante, Negros Occidental *Washington, a barangay in San Jacinto, Masbate *Washington, a barangay in Surigao City United States * Washington, Wisconsin (other) * Fort Washington (disambiguati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lyapunov Exponent
In mathematics, the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close trajectory, trajectories. Quantitatively, two trajectories in phase space with initial separation vector \delta \mathbf_0 diverge (provided that the divergence can be treated within the linearized approximation) at a rate given by : , \delta\mathbf(t) , \approx e^ , \delta \mathbf_0 , where \lambda is the Lyapunov exponent. The rate of separation can be different for different orientations of initial separation vector. Thus, there is a spectrum of Lyapunov exponents—equal in number to the dimensionality of the phase space. It is common to refer to the largest one as the maximal Lyapunov exponent (MLE), because it determines a notion of predictability for a dynamical system. A positive MLE is usually taken as an indication that the system is chaos theory, chaotic (provided some other conditions are m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eugene B
Eugene may refer to: People and fictional characters * Eugene (given name), including a list of people and fictional characters with the given name * Eugene (actress) (born 1981), Kim Yoo-jin, South Korean actress and former member of the singing group S.E.S. * Eugene (wrestler), professional wrestler Nick Dinsmore * Franklin Eugene (producer), American film producer * Gene Eugene, stage name of Canadian born actor, record producer, engineer, composer and musician Gene Andrusco (1961–2000) * Wendell Eugene (1923–2017), American jazz musician Places Canada * Mount Eugene, in Nunavut; the highest mountain of the United States Range on Ellesmere Island United States * Eugene, Oregon, a city ** Eugene, OR Metropolitan Statistical Area ** Eugene (Amtrak station) * Eugene Apartments, NRHP-listed apartment complex in Portland, Oregon * Eugene, Indiana, an unincorporated town * Eugene, Missouri, an unincorporated town Business * Eugene Green Energy Standard, an int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Washington Post
''The Washington Post'' (also known as the ''Post'' and, informally, ''WaPo'') is an American daily newspaper published in Washington, D.C. It is the most widely circulated newspaper within the Washington metropolitan area and has a large national audience. Daily broadsheet editions are printed for D.C., Maryland, and Virginia. The ''Post'' was founded in 1877. In its early years, it went through several owners and struggled both financially and editorially. Financier Eugene Meyer (financier), Eugene Meyer purchased it out of bankruptcy in 1933 and revived its health and reputation, work continued by his successors Katharine Graham, Katharine and Phil Graham (Meyer's daughter and son-in-law), who bought out several rival publications. The ''Post'' 1971 printing of the Pentagon Papers helped spur opposition to the Vietnam War. Subsequently, in the best-known episode in the newspaper's history, reporters Bob Woodward and Carl Bernstein led the American press's investigation into ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the '' Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of International Congresses Of Mathematicians Plenary And Invited Speakers
This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." The current list of Plenary and Invited Speakers presented here is based on the ICM's post-WW II terminology, in which the one-hour speakers in the morning sessions are called "Plenary Speakers" and the other speakers (in the afternoon sessions) whose talks are included in the ICM published proceedings are called "Invited Speakers". In the pre-WW II congresses the Plenary Speakers were called "Invited Speakers". By congress year 1897, Zürich * Jules Andrade *Léon Autonne *Émile Borel * N. V. Bougaïev * Francesco Brioschi * Hermann Brunn *Cesare Burali-Forti * Charles Jean de la Vallée Poussin * Gustaf Eneström *Federigo Enriques * Gino Fano * Zoel García de Galdeano * Francesco Gerbaldi * Paul Gordan * Jacques Hadamard * Adolf Hu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Modern Dynamics
The ''Journal of Modern Dynamics'' is a peer-reviewed scientific journal of mathematics published by the American Institute of Mathematical Sciences with the support of the Anatole Katok Center for Dynamical Systems and Geometry (Pennsylvania State University). The editor-in-chief is Giovanni Forni (University of Maryland College Park History The journal was established in 2007 with Anatole Katok as the founding editor-in-chief. It covers the theory of dynamical systems with particular emphasis on the mutual interaction between dynamics and other major areas of mathematical research: number theory, symplectic geometry, differential geometry, rigidity, quantum chaos, Teichmüller theory, geometric group theory, and harmonic analysis on manifolds. Until 2015 the journal was published quarterly. Since then, accepted papers are published online first and a single printed volume is published yearly. Abstracting and indexing The journal is abstracted and indexed in: *Current Contents/ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of California, Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant university and the founding campus of the University of California system. Its fourteen colleges and schools offer over 350 degree programs and enroll some 31,800 undergraduate and 13,200 graduate students. Berkeley ranks among the world's top universities. A founding member of the Association of American Universities, Berkeley hosts many leading research institutes dedicated to science, engineering, and mathematics. The university founded and maintains close relationships with three national laboratories at Berkeley, Livermore and Los Alamos, and has played a prominent role in many scientific advances, from the Manhattan Project and the discovery of 16 chemical elements to breakthroughs in computer science and genomics. Berkeley is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rufus Bowen
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 partitions, and invariant measures "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, California, 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, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lie Groups
In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additional properties it must have to be thought of as a "transformation" in the abstract sense, for instance multiplication and the taking of inverses (division), or equivalently, the concept of addition and the taking of inverses (subtraction). Combining these two ideas, one obtains a continuous group where multiplying points and their inverses are continuous. If the multiplication and taking of inverses are smooth (differentiable) as well, one obtains a Lie group. Lie groups provide a natural model for the concept of continuous symmetry, a celebrated example of which is the rotational symmetry in three dimensions (given by the special orthogonal group \text(3)). Lie groups are widely used in many parts of modern mathematics and physics. Li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abelian Groups
In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commutative. With addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples. Abelian groups are named after early 19th century mathematician Niels Henrik Abel. The concept of an abelian group underlies many fundamental algebraic structures, such as fields, rings, vector spaces, and algebras. The theory of abelian groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood and fully classified. Definition An abelian group is a set A, together with an operation \cdot that combines any two elements a and b of A to form another element of A, denoted a \cdot b. The sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diophantine Approximation
In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria. The first problem was to know how well a real number can be approximated by rational numbers. For this problem, a rational number ''a''/''b'' is a "good" approximation of a real number ''α'' if the absolute value of the difference between ''a''/''b'' and ''α'' may not decrease if ''a''/''b'' is replaced by another rational number with a smaller denominator. This problem was solved during the 18th century by means of continued fractions. Knowing the "best" approximations of a given number, the main problem of the field is to find sharp upper and lower bounds of the above difference, expressed as a function of the denominator. It appears that these bounds depend on the nature of the real numbers to be approximated: the lower bound for the approximation of a rational number by another rational number is larger tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
