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In computation theory, the Blum–Shub–Smale machine, or BSS machine, is a model of computation introduced by Lenore Blum, Michael Shub and Stephen Smale, intended to describe computations over the real numbers. [1]
The introduction of the book reprints the paper "Complexity and real computation: a manifesto", previously published by the same authors. This manifesto explains why classical discrete models of computation such as the Turing machine are inadequate for the study of numerical problems in areas such as scientific computing and computational geometry, motivating the newer model studied in the book.
Smale's problems is a list of eighteen unsolved problems in mathematics proposed by Steve Smale in 1998 [1] and republished in 1999. [2] Smale composed this list in reply to a request from Vladimir Arnold, then vice-president of the International Mathematical Union, who asked several mathematicians to propose a list of problems for the 21st century.
Stephen Smale (born July 15, 1930) is an American mathematician, known for his research in topology, dynamical systems and mathematical economics.He was awarded the Fields Medal in 1966 [2] and spent more than three decades on the mathematics faculty of the University of California, Berkeley (1960–1961 and 1964–1995), where he currently is Professor Emeritus, with research interests in ...
Blum is also known for the Blum–Shub–Smale machine, a theoretical model of computation over the real numbers. Blum and her co-authors, Michael Shub and Stephen Smale , showed that (analogously to the theory of Turing machines ) one can define analogues of NP-completeness , undecidability , and universality for this model.
Axiom A diffeomorphisms generalize Morse–Smale systems, which satisfy further restrictions (finitely many periodic points and transversality of stable and unstable submanifolds). Smale horseshoe map is an axiom A diffeomorphism with infinitely many periodic points and positive topological entropy .
The term "veridical paradox" applies perhaps more appropriately at this level: until Smale's work, there was no documented attempt to argue for or against the eversion of S 2, and later efforts are in hindsight, so there never was a historical paradox associated with sphere eversion, only an appreciation of the subtleties in visualizing it by ...
The Smale horseshoe map f is the composition of three geometrical transformations Mixing in a real ball of colored putty after consecutive iterations of Smale horseshoe map. In the mathematics of chaos theory, a horseshoe map is any member of a class of chaotic maps of the square into itself. It is a core example in the study of dynamical systems.
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