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57 relations: A Mathematical Theory of Communication, American Mathematical Society, Anosov diffeomorphism, Arithmetic dynamics, Artin billiard, Axiom A, Benjamin Weiss, Cambridge University Press, Claude Shannon, Complex dynamics, Continuous function, Cover (topology), Curvature, Data storage, Data transmission, Differential equation, Discrete time and continuous time, Dynamical system, Emil Artin, Geodesic, George David Birkhoff, Gibbs measure, Granularity, Gustav A. Hedlund, Heteroclinic orbit, Homoclinic orbit, Information theory, Jacques Hadamard, Jakob Nielsen (mathematician), John Edensor Littlewood, Journal de Mathématiques Pures et Appliquées, Linear algebra, Marina Ratner, Markov partition, Marston Morse, Mary Cartwright, Mathematics, Measure-preserving dynamical system, Norman Levinson, Paul Koebe, Pekka Myrberg, Periodic point, Proceedings of the National Academy of Sciences of the United States of America, Providence, Rhode Island, Quantum state, Roy Adler, Rufus Bowen, Sequence, Sharkovskii's theorem, Shift operator, ..., Shift space, Springer Science+Business Media, String (computer science), Subshift of finite type, Surface (topology), World Scientific, Yakov Sinai. Expand index (7 more) »
A Mathematical Theory of Communication
"A Mathematical Theory of Communication" is an article by mathematician Claude E. Shannon published in Bell System Technical Journal in 1948.
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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.
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Anosov diffeomorphism
In mathematics, more particularly in the fields of dynamical systems and geometric topology, an Anosov map on a manifold M is a certain type of mapping, from M to itself, with rather clearly marked local directions of "expansion" and "contraction".
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Arithmetic dynamics
Arithmetic dynamics is a field that amalgamates two areas of mathematics, dynamical systems and number theory.
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Artin billiard
In mathematics and physics, the Artin billiard is a type of a dynamical billiard first studied by Emil Artin in 1924.
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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.
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Benjamin Weiss
Benjamin Weiss (בנימין ווייס.; born 1941 in New York City) is an American-Israeli mathematician known for his contributions to Ergodic Theory, Topological dynamics, Probability theory, Game Theory, Descriptive set theory.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Claude Shannon
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as "the father of information theory".
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Complex dynamics
Complex dynamics is the study of dynamical systems defined by iteration of functions on complex number spaces.
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Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
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Cover (topology)
In mathematics, a cover of a set X is a collection of sets whose union contains X as a subset.
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Curvature
In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry.
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Data storage
Data storage is the recording (storing) of information (data) in a storage medium.
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Data transmission
Data transmission (also data communication or digital communications) is the transfer of data (a digital bitstream or a digitized analog signal) over a point-to-point or point-to-multipoint communication channel.
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Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives.
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Discrete time and continuous time
In mathematics and in particular mathematical dynamics, discrete time and continuous time are two alternative frameworks within which to model variables that evolve over time.
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Dynamical system
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space.
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Emil Artin
Emil Artin (March 3, 1898 – December 20, 1962) was an Austrian mathematician of Armenian descent.
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Geodesic
In differential geometry, a geodesic is a generalization of the notion of a "straight line" to "curved spaces".
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George David Birkhoff
George David Birkhoff (March 21, 1884 – November 12, 1944) was an American mathematician best known for what is now called the ergodic theorem.
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Gibbs measure
In mathematics, the Gibbs measure, named after Josiah Willard Gibbs, is a probability measure frequently seen in many problems of probability theory and statistical mechanics.
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Granularity
Granularity (also called graininess), the condition of existing in grains or granules, refers to the extent to which a material or system is composed of distinguishable pieces or grains.
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Gustav A. Hedlund
Gustav Arnold Hedlund (May 7, 1904 – March 15, 1993), an American mathematician, was one of the founders of symbolic and topological dynamics.
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Heteroclinic orbit
In mathematics, in the phase portrait of a dynamical system, a heteroclinic orbit (sometimes called a heteroclinic connection) is a path in phase space which joins two different equilibrium points.
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Homoclinic orbit
In mathematics, a homoclinic orbit is a trajectory of a flow of a dynamical system which joins a saddle equilibrium point to itself.
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Information theory
Information theory studies the quantification, storage, and communication of information.
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Jacques Hadamard
Jacques Salomon Hadamard ForMemRS (8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex function theory, differential geometry and partial differential equations.
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Jakob Nielsen (mathematician)
Jakob Nielsen (15 October 1890 in Mjels, Als – 3 August 1959 in Helsingør) was a Danish mathematician known for his work on automorphisms of surfaces.
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John Edensor Littlewood
John Edensor Littlewood FRS LLD (9 June 1885 – 6 September 1977) was an English mathematician.
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Journal de Mathématiques Pures et Appliquées
The Journal de Mathématiques Pures et Appliquées is a French monthly scientific journal of mathematics, founded in 1836 by Joseph Liouville (editor: 1836–1874).
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Linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.
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Marina Ratner
Marina Evseevna Ratner (Мари́на Евсе́евна Ра́тнер; October 30, 1938 – July 7, 2017) was a professor of mathematics at the University of California, Berkeley who worked in ergodic theory.
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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 dynamics.
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Marston Morse
Harold Calvin Marston Morse (March 24, 1892 – June 22, 1977) was an American mathematician best known for his work on the calculus of variations in the large, a subject where he introduced the technique of differential topology now known as Morse theory.
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Mary Cartwright
Dame Mary Lucy Cartwright, (17 December 1900 – 3 April 1998) was a British mathematician.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Measure-preserving dynamical system
In mathematics, a measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular.
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Norman Levinson
Norman Levinson (August 11, 1912 in Lynn, Massachusetts – October 10, 1975 in Boston) was an American mathematician.
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Paul Koebe
Paul Koebe (15 February 1882 – 6 August 1945) was a 20th-century German mathematician.
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Pekka Myrberg
Pekka Juhana Myrberg (30 December 1892, Viipuri – 8 November 1976, Helsinki) was a Finnish mathematician known for developing the concept of period-doubling in a paper published in the 1950s.
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Periodic point
In mathematics, in the study of iterated functions and dynamical systems, a periodic point of a function is a point which the system returns to after a certain number of function iterations or a certain amount of time.
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Proceedings of the National Academy of Sciences of the United States of America
Proceedings of the National Academy of Sciences of the United States of America (PNAS) is the official scientific journal of the National Academy of Sciences, published since 1915.
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Providence, Rhode Island
Providence is the capital and most populous city of the U.S. state of Rhode Island and is one of the oldest cities in the United States.
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Quantum state
In quantum physics, quantum state refers to the state of an isolated quantum system.
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Roy Adler
Roy Lee Adler (February 22, 1931 – July 26, 2016) was an American mathematician.
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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.
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Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.
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Sharkovskii's theorem
In mathematics, Sharkovskii's theorem, named after Oleksandr Mykolaiovych Sharkovskii who published it in 1964, is a result about discrete dynamical systems.
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Shift operator
In mathematics, and in particular functional analysis, the shift operator also known as translation operator is an operator that takes a function to its translation.
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Shift space
In symbolic dynamics and related branches of mathematics, a shift space or subshift is a set of infinite words that represent the evolution of a discrete system.
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Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
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String (computer science)
In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable.
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Subshift of finite type
In mathematics, subshifts of finite type are used to model dynamical systems, and in particular are the objects of study in symbolic dynamics and ergodic theory.
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Surface (topology)
In topology and differential geometry, a surface is a two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space.
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World Scientific
World Scientific Publishing is an academic publisher of scientific, technical, and medical books and journals headquartered in Singapore.
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Yakov Sinai
Yakov Grigorevich Sinai (Я́ков Григо́рьевич Сина́й; born September 21, 1935) is a mathematician known for his work on dynamical systems.
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References
[1] https://en.wikipedia.org/wiki/Symbolic_dynamics
