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## Smale, Steve

Compute Distance To:
 Author ID: smale.steve Published as: Smale, S.; Smale, Stephan; Smale, Stephen; Smale, Steve; Smale, Steven Homepage: http://ttic.uchicago.edu/~smale/vita.html External Links: MGP · Math-Net.Ru · Wikidata · dblp · GND · MacTutor Awards: Fields Medal (1966) · Wolf Prize (2007)
 Documents Indexed: 157 Publications since 1957, including 11 Books Biographic References: 19 Publications
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#### Co-Authors

 88 single-authored 19 Shub, Michael 12 Cucker, Felipe 10 Zhou, Dingxuan 6 Blum, Lenore 5 Hirsch, Morris W. 3 Chern, Shiing-Shen 3 Jetter, Kurt 3 Niyogi, Partha 3 Poggio, Tomaso A. 3 Rajapakse, Indika 3 Weinberger, Shmuel 2 Caponnetto, Andrea 2 Devaney, Robert L. 2 Lashof, Richard K. 2 Smale, Nathan 1 Abraham, Ralph Herman 1 Bartholdi, Laurent 1 Berry, Michael Victor 1 Bouvrie, Jake 1 Christmann, Andreas 1 Dedieu, Jean-Pierre 1 Guo, Xin 1 Gurdian, Rodolfo 1 Jaffe, Arthur Michael 1 Khesin, Boris A. 1 Khovanskiĭ, Askold Georgievich 1 Koiran, Pascal 1 Mumford, David Bryant 1 Palais, Richard S. 1 Palis, Jacob jun. 1 Renegar, James 1 Rosasco, Lorenzo A. 1 Schick, Thomas 1 Sevryuk, Mikhail Borisovich 1 Shen, Wenjun 1 Tabachnikov, Serge L. 1 Tu, Loring W. 1 Varchenko, Alexander Nikolaevich 1 Williams, Robert F. 1 Wong, Hau-San 1 Xiao, Quanwu 1 Yao, Yuan 1 Yau, Shing-Tung 1 Zhou, Ding-Xuan
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#### Serials

 8 Annals of Mathematics. Second Series 8 Foundations of Computational Mathematics 7 Journal of Mathematical Economics 6 Bulletin of the American Mathematical Society. New Series 4 American Journal of Mathematics 4 Journal of Complexity 4 Analysis and Applications (Singapore) 4 Bulletin of the American Mathematical Society 3 Uspekhi Matematicheskikh Nauk [N. S.] 3 The Mathematical Intelligencer 3 Proceedings of the American Mathematical Society 3 Notices of the American Mathematical Society 3 Oberwolfach Reports 3 Proceedings of Symposia in Pure Mathematics 2 Journal of Mathematical Biology 2 Inventiones Mathematicae 2 SIAM Journal on Computing 2 Theoretical Computer Science 2 Transactions of the American Mathematical Society 2 Constructive Approximation 2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Journal of Mathematics and Mechanics 1 American Mathematical Monthly 1 Communications on Pure and Applied Mathematics 1 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV) 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Boletín de la Sociedad Matemática Mexicana. Segunda Serie 1 Commentarii Mathematici Helvetici 1 Duke Mathematical Journal 1 Econometrica 1 Gazette des Mathématiciens 1 IEEE Transactions on Automatic Control 1 Journal of Differential Geometry 1 Mathematical Programming 1 SIAM Journal on Numerical Analysis 1 Synthese 1 Physica D 1 Journal of Symbolic Computation 1 Discrete & Computational Geometry 1 Journal of the American Mathematical Society 1 Proceedings of the National Academy of Sciences of the United States of America 1 SIAM Review 1 Applied and Computational Harmonic Analysis 1 Journal of the ACM 1 La Gaceta de la Real Sociedad Matemática Española 1 Annali della Scuola Normale Superiore di Pisa. Scienze Fisiche e Matematiche. III. Ser 1 Mathematical Medley 1 Japanese Journal of Mathematics. 3rd Series
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#### Fields

 43 Computer science (68-XX) 28 Dynamical systems and ergodic theory (37-XX) 24 Numerical analysis (65-XX) 19 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 15 History and biography (01-XX) 14 Global analysis, analysis on manifolds (58-XX) 14 Statistics (62-XX) 13 Functions of a complex variable (30-XX) 13 Manifolds and cell complexes (57-XX) 9 General and overarching topics; collections (00-XX) 9 Operations research, mathematical programming (90-XX) 9 Biology and other natural sciences (92-XX) 8 Field theory and polynomials (12-XX) 8 Ordinary differential equations (34-XX) 8 Approximations and expansions (41-XX) 5 Mathematical logic and foundations (03-XX) 5 Mechanics of particles and systems (70-XX) 4 Partial differential equations (35-XX) 4 Probability theory and stochastic processes (60-XX) 4 Information and communication theory, circuits (94-XX) 3 Number theory (11-XX) 3 Real functions (26-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 2 Functional analysis (46-XX) 2 Algebraic topology (55-XX) 1 Algebraic geometry (14-XX) 1 Operator theory (47-XX) 1 Convex and discrete geometry (52-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH Open

136 Publications have been cited 8,389 times in 6,188 Documents Cited by Year
Differentiable dynamical systems. With an appendix to the first part of the paper: “Anosov diffeomorphisms” by John Mather. Zbl 0202.55202
Smale, S.
1967
Differential equations, dynamical systems, and linear algebra. Zbl 0309.34001
Hirsch, Morris W.; Smale, Stephen
1974
Emergent behavior in flocks. Zbl 1366.91116
Cucker, Felipe; Smale, Steve
2007
On the mathematical foundations of learning. Zbl 0983.68162
Cucker, Felipe; Smale, Steve
2002
Mathematical problems for the next century. Zbl 0947.01011
Smale, Steve
1998
On a theory of computation and complexity over the real numbers: NP- completeness, recursive functions and universal machines. Zbl 0681.03020
Blum, Lenore; Shub, Mike; Smale, Steve
1989
Complexity and real computation: A manifesto. Zbl 0872.68036
Blum, Lenore; Cucker, Felipe; Shub, Mike; Smale, Steve
1996
An infinite dimensional version of Sard’s theorem. Zbl 0143.35301
Smale, S.
1965
Learning theory estimates via integral operators and their approximations. Zbl 1127.68088
Smale, Steve; Zhou, Ding-Xuan
2007
Topology and mechanics. II: The planar $$n$$-body problem. Zbl 0203.26102
Smale, S.
1970
The fundamental theorem of algebra and complexity theory. Zbl 0456.12012
Smale, Steve
1981
Diffeomorphisms with many periodic points. Zbl 0142.41103
Smale, S.
1965
Differential equations, dynamical systems, and an introduction to chaos. 2nd ed. Zbl 1135.37002
Hirsch, Morris W.; Smale, Stephen; Devaney, Robert L.
2004
On the mathematics of emergence. Zbl 1166.92323
Cucker, Felipe; Smale, Steve
2007
Topology and mechanics. I. Zbl 0202.23201
Smale, S.
1970
Generalized Poincaré’s conjecture in dimensions greater than four. Zbl 0099.39202
Smale, Stephen
1961
Structural stability theorems. Zbl 0214.50702
Palis, J.; Smale, S.
1970
A convergent process of price adjustment and global Newton methods. Zbl 0354.90018
Smale, Steve
1976
On the efficiency of algorithms of analysis. Zbl 0592.65032
Smale, Steve
1985
Finding the homology of submanifolds with high confidence from random samples. Zbl 1148.68048
Niyogi, Partha; Smale, Stephen; Weinberger, Shmuel
2008
Complexity of Bezout’s theorem. I: Geometric aspects. Zbl 0821.65035
Shub, Michael; Smale, Steve
1993
Shannon sampling and function reconstruction from point values. Zbl 1107.94007
Smale, Steve; Zhou, Ding-Xuan
2004
On the structure of manifolds. Zbl 0109.41103
Smale, S.
1962
A generalized Morse theory. Zbl 0119.09201
Palais, R. S.; Smale, S.
1964
Diffeomorphisms of the 2-sphere. Zbl 0118.39103
Smale, S.
1959
On gradient dynamical systems. Zbl 0136.43702
Smale, S.
1961
Estimating the approximation error in learning theory. Zbl 1079.68089
Smale, Steve; Zhou, Ding-Xuan
2003
The classification of immersions of spheres in Euclidean spaces. Zbl 0089.18201
Smale, Stephen
1959
Complexity of Bezout’s theorem. II: Volumes and probabilities. Zbl 0851.65031
Shub, M.; Smale, S.
1993
Shannon sampling. II: Connections to learning theory. Zbl 1107.94008
Smale, Steve; Zhou, Ding-Xuan
2005
Best choices for regularization parameters in learning theory: on the bias-variance problem. Zbl 1057.68085
Cucker, Felipe; Smale, Steve
2002
Newton’s method estimates from data at one point. Zbl 0613.65058
Smale, Steve
1986
On the differential equations of species in competition. Zbl 0344.92009
Smale, S.
1976
Complexity of Bezout’s theorem. IV: Probability of success; extensions. Zbl 0843.65035
Shub, Michael; Smale, Steve
1996
Differential equations, dynamical systems, and an introduction to chaos. 3rd ed. Zbl 1239.37001
Hirsch, Morris W.; Smale, Stephen; Devaney, Robert L.
2013
Online learning with Markov sampling. Zbl 1170.68022
Smale, Steve; Zhou, Ding-Xuan
2009
Complexity of Bezout’s theorem. III: Condition number and packing. Zbl 0846.65018
Shub, Michael; Smale, Steve
1993
Morse inequalities for a dynamical system. Zbl 0100.29701
Smale, Stephen
1960
Mathematical problems for the next century. Zbl 1031.00005
Smale, Steve
2000
On the structure of 5-manifolds. Zbl 0101.16103
Smale, Stephen
1962
Complexity of Bezout’s theorem. V: Polynomial time. Zbl 0846.65022
Shub, M.; Smale, S.
1994
Complexity and real computation. Foreword by Richard M. Karp. Zbl 0948.68068
Blum, Leonore; Cucker, Felipe; Shub, Michael; Smale, Steve
1997
The mathematics of learning: dealing with data. Zbl 1083.68100
Poggio, Tomaso; Smale, Steve
2003
On the Morse index theorem. Zbl 0166.36102
Smale, S.
1965
On the average number of steps of the simplex method of linear programming. Zbl 0526.90060
Smale, Steve
1983
The mathematics of time. Essays on dynamical systems, economic processes, and related topics. Zbl 0451.58001
Smale, Steve
1980
Global analysis and economics. II: Extension of a theorem of Debreu. Zbl 0316.90006
Smale, S.
1974
Stable manifolds for differential equations and diffeomorphisms. Zbl 0113.29702
Smale, S.
1963
Morse theory and a non-linear generalization of the Dirichlet problem. Zbl 0131.32305
Smale, S.
1964
Complexity theory and numerical analysis. Zbl 0883.65125
Smale, Steve
1997
A Vietoris mapping theorem for homotopy. Zbl 0089.39003
Smale, Stephen
1957
On algorithms for solving f(x)=0. Zbl 0408.65032
Hirsch, Morris W.; Smale, Stephen
1979
Global analysis and economics. VI: Geometric analysis of Pareto optima and price equilibria under classical hypotheses. Zbl 0348.90017
Smale, S.
1976
Global analysis and economics. V: Pareto theory with constraints. Zbl 0357.90010
Smale, S.
1974
Structurally stable systems are not dense. Zbl 0149.20001
Smale, S.
1966
The prisoner’s dilemma and dynamical systems associated to non- cooperative games. Zbl 0463.90099
Smale, Steve
1980
Global analysis and economics. I: Pareto optimum and a generalization of Morse theory. Zbl 0269.58009
Smale, Steve
1973
On the mathematical foundations of electrical circuit theory. Zbl 0286.34071
Smale, S.
1972
Algorithms for solving equations. Zbl 0665.65058
Smale, Steve
1987
Computational complexity: On the geometry of polynomials and a theory of cost. II. Zbl 0625.65036
Shub, M.; Smale, S.
1986
A topological view of unsupervised learning from noisy data. Zbl 1230.62085
Niyogi, P.; Smale, S.; Weinberger, S.
2011
Online learning algorithms. Zbl 1119.68098
Smale, Steve; Yao, Yuan
2006
Dynamics retrospective: Great problems, attempts that failed. Zbl 0745.58018
Smale, Steve
1991
On the geometry of polynomials and a theory of cost. I. Zbl 0603.65027
Shub, Mike; Smale, Steve
1985
Global analysis and economics. III: Pareto Optima and price equilibria. Zbl 0316.90007
Smale, S.
1974
Nongenericity of $$\Omega$$-stability. Zbl 0215.25102
Abraham, R.; Smale, S.
1970
On the topology of algorithms. I. Zbl 0639.68042
Smale, Steve
1987
On the existence of generally convergent algorithms. Zbl 0595.65048
Shub, Michael; Smale, Steve
1986
Global analysis and economics. IV: Finiteness and stability of equilibria with general consumption sets and production. Zbl 0316.90008
Smale, S.
1974
Notes on differentiable dynamical systems. Zbl 0205.54201
Smale, S.
1970
Regular curves on Riemannian manifolds. Zbl 0081.38103
Smale, Stephen
1958
A mathematical model of two cells via Turing’s equation. Zbl 0333.92002
Smale, S.
1974
A classification of immersions of the two-sphere. Zbl 0089.18102
Smale, Stephen
1959
Geometry on probability spaces. Zbl 1187.68270
Smale, Steve; Zhou, Ding-Xuan
2009
On the immersion of manifolds in Euclidean space. Zbl 0097.38805
Lashof, R.; Smale, S.
1958
Exchange processes with price adjustment. Zbl 0366.90013
Smale, Stephen
1976
Complexity estimates depending on condition and round-off error. Zbl 1065.68533
Cucker, Felipe; Smale, Steve
1999
Modeling language evolution. Zbl 1083.68131
Cucker, Felipe; Smale, Steve; Zhou, Ding-Xuan
2004
The qualitative analysis of a difference equation of population growth. Zbl 0342.92014
Smale, S.; Williams, R. F.
1976
Finding a horseshoe on the beaches of Rio. Zbl 0983.37001
Smale, Steve
1998
On the intractability of Hilbert’s Nullstellensatz and an algebraic version of “$$NP\neq P$$?”. Zbl 0882.03040
Shub, Michael; Smale, Steve
1995
The $$\Omega$$-stability theorem. Zbl 0205.54104
Smale, S.
1970
Global analysis and economics. Zbl 0477.90014
Smale, Steve
1981
Separation of complexity classes in Koiran’s weak model. Zbl 0819.68053
Cucker, F.; Shub, M.; Smale, S.
1994
Some remarks on the foundations of numerical analysis. Zbl 0703.65003
Smale, Steve
1990
Smooth solutions of the heat and wave equations. Zbl 0439.35017
Smale, Stephen
1980
Beyond hyperbolicity. Zbl 0247.58008
Shub, M.; Smale, S.
1972
The generalized Poincaré conjecture in higher dimensions. Zbl 0099.39201
Smale, Stephen
1960
A polynomial time algorithm for diophantine equations in one variable. Zbl 0920.11085
Cucker, Felipe; Koiran, Pascal; Smale, Steve
1999
Algebraic settings for the problem ”P$$\neq$$NP?”. Zbl 0856.68068
Blum, Lenore; Cucker, Felipe; Shub, Mike; Smale, Steve
1996
On the problem of reviving the ergodic hypothesis of Boltzmann and Birkhoff. Zbl 0486.58014
Smale, S.
1980
The problem of the average speed of the simplex method. Zbl 0552.90059
Smale, S.
1983
Global analysis and economics. I: Pareto optimum and a generalisation of Morse theory. Zbl 0267.58008
Smale, S.
1972
Self-intersections of immersed manifolds. Zbl 0093.37501
Lashof, R. K.; Smale, S.
1959
Hodge theory on metric spaces. Appendix by Anthony W. Baker. Zbl 1366.58001
Bartholdi, Laurent; Schick, Thomas; Smale, Nat; Smale, Steve
2012
On a theory of computation over the real numbers; NP completeness, recursive functions and universal machines. Zbl 0691.68034
Blum, L.; Shub, M.; Smale, S.
1990
Optimizing several functions. Zbl 0349.90086
Smale, Stephen
1975
Differentiable and combinatorial structures on manifolds. Zbl 0111.18902
Smale, Stephen
1961
Problems on the nature of relative equilibria in celestial mechanics. Zbl 0215.52602
Smale, S.
1971
Stable manifolds for differential equations and diffeomorphisms. Zbl 0202.55201
Smale, S.
1962
Mathematics of the genome. Zbl 1380.37148
Rajapakse, Indika; Smale, Steve
2017
The pitchfork bifurcation. Zbl 1373.34058
Rajapakse, Indika; Smale, Steve
2017
Emergence of function from coordinated cells in a tissue. Zbl 1404.92067
Rajapakse, Indika; Smale, Stephen
2017
Introduction to the peptide binding problem of computational immunology: new results. Zbl 1329.92096
Shen, Wen-Jun; Wong, Hau-San; Xiao, Quan-Wu; Guo, Xin; Smale, Stephen
2014
Differential equations, dynamical systems, and an introduction to chaos. 3rd ed. Zbl 1239.37001
Hirsch, Morris W.; Smale, Stephen; Devaney, Robert L.
2013
Hodge theory on metric spaces. Appendix by Anthony W. Baker. Zbl 1366.58001
Bartholdi, Laurent; Schick, Thomas; Smale, Nat; Smale, Steve
2012
Abstract and classical Hodge-de Rham theory. Zbl 1243.58003
Smale, Nat; Smale, Steve
2012
A topological view of unsupervised learning from noisy data. Zbl 1230.62085
Niyogi, P.; Smale, S.; Weinberger, S.
2011
Mathematics of the neural response. Zbl 1185.68813
Smale, S.; Rosasco, L.; Bouvrie, J.; Caponnetto, A.; Poggio, T.
2010
Online learning with Markov sampling. Zbl 1170.68022
Smale, Steve; Zhou, Ding-Xuan
2009
Geometry on probability spaces. Zbl 1187.68270
Smale, Steve; Zhou, Ding-Xuan
2009
Finding the homology of submanifolds with high confidence from random samples. Zbl 1177.62003
Niyogi, Partha; Smale, Stephen; Weinberger, Shmuel
2009
Finding the homology of submanifolds with high confidence from random samples. Zbl 1148.68048
Niyogi, Partha; Smale, Stephen; Weinberger, Shmuel
2008
Learning theory and approximation. Abstracts from the workshop held June 29 – July 5, 2008. Zbl 1177.68114
Jetter, Kurt (ed.); Smale, Steve (ed.); Zhou, Ding-Xuan (ed.)
2008
Emergent behavior in flocks. Zbl 1366.91116
Cucker, Felipe; Smale, Steve
2007
Learning theory estimates via integral operators and their approximations. Zbl 1127.68088
Smale, Steve; Zhou, Ding-Xuan
2007
On the mathematics of emergence. Zbl 1166.92323
Cucker, Felipe; Smale, Steve
2007
Risk bounds for random regression graphs. Zbl 1368.68278
Caponnetto, A.; Smale, S.
2007
Online learning algorithms. Zbl 1119.68098
Smale, Steve; Yao, Yuan
2006
Shannon sampling. II: Connections to learning theory. Zbl 1107.94008
Smale, Steve; Zhou, Ding-Xuan
2005
On problems of computational complexity. Zbl 1147.68527
Smale, Stephen
2005
Differential equations, dynamical systems, and an introduction to chaos. 2nd ed. Zbl 1135.37002
Hirsch, Morris W.; Smale, Stephen; Devaney, Robert L.
2004
Shannon sampling and function reconstruction from point values. Zbl 1107.94007
Smale, Steve; Zhou, Ding-Xuan
2004
Modeling language evolution. Zbl 1083.68131
Cucker, Felipe; Smale, Steve; Zhou, Ding-Xuan
2004
Estimating the approximation error in learning theory. Zbl 1079.68089
Smale, Steve; Zhou, Ding-Xuan
2003
The mathematics of learning: dealing with data. Zbl 1083.68100
Poggio, Tomaso; Smale, Steve
2003
On the mathematical foundations of learning. Zbl 0983.68162
Cucker, Felipe; Smale, Steve
2002
Best choices for regularization parameters in learning theory: on the bias-variance problem. Zbl 1057.68085
Cucker, Felipe; Smale, Steve
2002
Mathematical problems for the next century. Zbl 1031.00005
Smale, Steve
2000
Mathematical problems of the next century. Zbl 1077.01502
Smale, S.
2000
The collected papers of Stephen Smale. Vols. 1-3. Edited by F. Cucker and R. Wong. Zbl 0995.01005
Smale, Stephen
2000
Mathematical problems for the next century. Zbl 1040.01006
Smale, Steve
2000
Complexity estimates depending on condition and round-off error. Zbl 1065.68533
Cucker, Felipe; Smale, Steve
1999
A polynomial time algorithm for diophantine equations in one variable. Zbl 0920.11085
Cucker, Felipe; Koiran, Pascal; Smale, Steve
1999
Mathematical problems for the next century. Zbl 0947.01011
Smale, Steve
1998
Finding a horseshoe on the beaches of Rio. Zbl 0983.37001
Smale, Steve
1998
Some lower bounds for the complexity of continuation methods. Zbl 0918.65038
Dedieu, Jean-Pierre; Smale, Steve
1998
The work of Curtis T. McMullen. Zbl 1288.01063
Smale, Steven
1998
Complexity and real computation. Foreword by Richard M. Karp. Zbl 0948.68068
Blum, Leonore; Cucker, Felipe; Shub, Michael; Smale, Steve
1997
Complexity theory and numerical analysis. Zbl 0883.65125
Smale, Steve
1997
Complexity and real computation: A manifesto. Zbl 0872.68036
Blum, Lenore; Cucker, Felipe; Shub, Mike; Smale, Steve
1996
Complexity of Bezout’s theorem. IV: Probability of success; extensions. Zbl 0843.65035
Shub, Michael; Smale, Steve
1996
Algebraic settings for the problem ”P$$\neq$$NP?”. Zbl 0856.68068
Blum, Lenore; Cucker, Felipe; Shub, Mike; Smale, Steve
1996
On the intractability of Hilbert’s Nullstellensatz and an algebraic version of “$$NP\neq P$$?”. Zbl 0882.03040
Shub, Michael; Smale, Steve
1995
Complexity of Bezout’s theorem. V: Polynomial time. Zbl 0846.65022
Shub, M.; Smale, S.
1994
Separation of complexity classes in Koiran’s weak model. Zbl 0819.68053
Cucker, F.; Shub, M.; Smale, S.
1994
Complexity of Bezout’s theorem. I: Geometric aspects. Zbl 0821.65035
Shub, Michael; Smale, Steve
1993
Complexity of Bezout’s theorem. II: Volumes and probabilities. Zbl 0851.65031
Shub, M.; Smale, S.
1993
Complexity of Bezout’s theorem. III: Condition number and packing. Zbl 0846.65018
Shub, Michael; Smale, Steve
1993
The Gödel incompleteness theorem and decidability over a ring. Zbl 0793.03066
Blum, Lenore; Smale, Steve
1993
Dynamics retrospective: Great problems, attempts that failed. Zbl 0745.58018
Smale, Steve
1991
Some remarks on the foundations of numerical analysis. Zbl 0703.65003
Smale, Steve
1990
On a theory of computation over the real numbers; NP completeness, recursive functions and universal machines. Zbl 0691.68034
Blum, L.; Shub, M.; Smale, S.
1990
The story of the higher dimensional Poincaré conjecture (what actually happened on the beaches of Rio). Zbl 0703.57001
Smale, Steve
1990
On a theory of computation and complexity over the real numbers: NP- completeness, recursive functions and universal machines. Zbl 0681.03020
Blum, Lenore; Shub, Mike; Smale, Steve
1989
Algorithms for solving equations. Zbl 0665.65058
Smale, Steve
1987
On the topology of algorithms. I. Zbl 0639.68042
Smale, Steve
1987
Newton’s method estimates from data at one point. Zbl 0613.65058
Smale, Steve
1986
Computational complexity: On the geometry of polynomials and a theory of cost. II. Zbl 0625.65036
Shub, M.; Smale, S.
1986
On the existence of generally convergent algorithms. Zbl 0595.65048
Shub, Michael; Smale, Steve
1986
On the efficiency of algorithms of analysis. Zbl 0592.65032
Smale, Steve
1985
On the geometry of polynomials and a theory of cost. I. Zbl 0603.65027
Shub, Mike; Smale, Steve
1985
On the average number of steps of the simplex method of linear programming. Zbl 0526.90060
Smale, Steve
1983
The problem of the average speed of the simplex method. Zbl 0552.90059
Smale, S.
1983
On the average cost of solving polynomial equations. Zbl 0529.41008
Shub, Mike; Smale, Steve
1983
The fundamental theorem of algebra and complexity theory. Zbl 0456.12012
Smale, Steve
1981
Global analysis and economics. Zbl 0477.90014
Smale, Steve
1981
The mathematics of time. Essays on dynamical systems, economic processes, and related topics. Zbl 0451.58001
Smale, Steve
1980
The prisoner’s dilemma and dynamical systems associated to non- cooperative games. Zbl 0463.90099
Smale, Steve
1980
Smooth solutions of the heat and wave equations. Zbl 0439.35017
Smale, Stephen
1980
On the problem of reviving the ergodic hypothesis of Boltzmann and Birkhoff. Zbl 0486.58014
Smale, S.
1980
On algorithms for solving f(x)=0. Zbl 0408.65032
Hirsch, Morris W.; Smale, Stephen
1979
On comparative statics and bifurcation in economic equilibrium theory. Zbl 0437.90026
Smale, Steve
1979
An approach to the analysis of dynamic processes in economic systems. Zbl 0387.90031
Smale, Steve
1978
Convergent process of price adjustment and global Newton methods. Zbl 0384.34025
Smale, Steve
1977
Dynamical systems and turbulence. Zbl 0362.58012
Smale, Steve
1977
A convergent process of price adjustment and global Newton methods. Zbl 0354.90018
Smale, Steve
1976
On the differential equations of species in competition. Zbl 0344.92009
Smale, S.
1976
Global analysis and economics. VI: Geometric analysis of Pareto optima and price equilibria under classical hypotheses. Zbl 0348.90017
Smale, S.
1976
Exchange processes with price adjustment. Zbl 0366.90013
Smale, Stephen
1976
The qualitative analysis of a difference equation of population growth. Zbl 0342.92014
Smale, S.; Williams, R. F.
1976
Optimizing several functions. Zbl 0349.90086
Smale, Stephen
1975
Sufficient conditions for an optimum. Zbl 0314.58007
Smale, S.
1975
Global analysis and economics. Pareto optimum and a generalization of Morse theory. Zbl 0312.90007
Smale, Steve
1975
Differential equations, dynamical systems, and linear algebra. Zbl 0309.34001
Hirsch, Morris W.; Smale, Stephen
1974
Global analysis and economics. II: Extension of a theorem of Debreu. Zbl 0316.90006
Smale, S.
1974
Global analysis and economics. V: Pareto theory with constraints. Zbl 0357.90010
Smale, S.
1974
Global analysis and economics. III: Pareto Optima and price equilibria. Zbl 0316.90007
Smale, S.
1974
Global analysis and economics. IV: Finiteness and stability of equilibria with general consumption sets and production. Zbl 0316.90008
Smale, S.
1974
A mathematical model of two cells via Turing’s equation. Zbl 0333.92002
Smale, S.
1974
Global analysis and economics. I: Pareto optimum and a generalization of Morse theory. Zbl 0269.58009
Smale, Steve
1973
Stability and isotopy in discrete dynamical systems. Zbl 0284.58013
Smale, Steve
1973
On the mathematical foundations of electrical circuit theory. Zbl 0286.34071
Smale, S.
1972
Beyond hyperbolicity. Zbl 0247.58008
Shub, M.; Smale, S.
1972
Global analysis and economics. I: Pareto optimum and a generalisation of Morse theory. Zbl 0267.58008
Smale, S.
1972
Topology and mechanics. Zbl 0233.57018
Smale, S.
1972
Problems on the nature of relative equilibria in celestial mechanics. Zbl 0215.52602
Smale, S.
1971
Topology and mechanics. II: The planar $$n$$-body problem. Zbl 0203.26102
Smale, S.
1970
Topology and mechanics. I. Zbl 0202.23201
Smale, S.
1970
Structural stability theorems. Zbl 0214.50702
Palis, J.; Smale, S.
1970
...and 36 more Documents
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#### Cited by 6,990 Authors

 70 Ha, Seung-Yeal 51 Llibre, Jaume 49 Grines, Vyacheslav Zigmundovich 49 Zhou, Dingxuan 44 Cucker, Felipe 41 Smale, Steve 39 Pochinka, Olga Vital’evna 34 Shub, Michael 26 Zhuzhoma, Evgeniĭ Viktorovich 25 Choi, Young-Pil 24 Medvedev, Vladislav Sergeevich 23 Carrillo de la Plata, José Antonio 23 Marsden, Jerrold Eldon 23 Sun, Hongwei 22 Beltrán, Carlos 22 Chen, Dirong 22 Yu, Pei 21 Koiran, Pascal 21 Meer, Klaus 20 Pardo, Luis Miguel 20 Petković, Miodrag S. 19 Bürgisser, Peter 19 Han, Maoan 19 Hirsch, Morris W. 19 Sheng, Baohuai 18 Mello, Luis Fernando O. 18 Xiang, Dao-Hong 17 Degond, Pierre 17 Holmes, Philip J. 17 Pillonetto, Gianluigi 17 Ruelle, David Pierre 16 Argyros, Ioannis Konstantinos 16 Bonatti, Christian 16 Kim, Jeongho 16 Laudenbach, François 15 Guo, Zheng-Chu 14 Kuznetsov, Sergey P. 14 Li, Chong 14 Li, Luoqing 14 Wu, Qiang 14 Xu, Zongben 13 Chen, Guanrong 13 Chen, Hong 13 Fernandes, Antonio Carlos 13 Jørgensen, Palle E. T. 13 Rosasco, Lorenzo A. 13 Shi, Lei 13 Tong, Hongzhi 13 Yorke, James Alan 13 Zhang, Xiongtao 12 Basu, Saugata 12 Dedieu, Jean-Pierre 12 Dong, Jiu-Gang 12 Fornasier, Massimo 12 Hu, Ting 12 Li, Jibin 12 Malajovich, Gregorio 12 Palis, Jacob jun. 12 Sanguineti, Marcello 11 Chazal, Frédéric 11 Devaney, Robert L. 11 Ferreira, Orizon Pereira 11 Gutiérrez, José Manuel 11 Kim, Doheon 11 Li, Zhuchun 11 Pérez-Chavela, Ernesto 11 Pugh, Charles Chapman 11 Temam, Roger Meyer 10 Armentano, Diego 10 Bellomo, Nicola 10 Block, Louis Stuart 10 Bowen, Rufus 10 Crovisier, Sylvain 10 Gnecco, Giorgio 10 Guckenheimer, John M. 10 Gurevich, Elena Ya. 10 Kim, Dohyun 10 Pan, Victor Yakovlevich 10 Rančić, Lidija Z. 10 Robinson, Clark 10 Santoprete, Manuele 10 Wang, Qiudong 10 Xian, Jun 10 Zhang, Haizhang 10 Zou, Bin 9 Bournez, Olivier 9 Campagnolo, Manuel Lameiras 9 Cao, Feilong 9 De Vito, Ernesto 9 Diacu, Florin Nicolae 9 Fiedler, Bernold 9 Graça, Daniel Silva 9 Lv, Shaogao 9 Malinowska, Agnieszka Barbara 9 Petković, Ljiljana D. 9 Rojas, J. Maurice 9 Shamolin, Maksim Vladimirovich 9 Straughan, Brian 9 Tadmor, Eitan 9 Takens, Floris ...and 6,890 more Authors
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#### Cited in 666 Serials

 202 Journal of Differential Equations 179 Transactions of the American Mathematical Society 160 Journal of Complexity 121 Journal of Mathematical Analysis and Applications 113 Theoretical Computer Science 111 Physica D 108 Proceedings of the American Mathematical Society 106 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 92 Journal of Mathematical Economics 80 Applied Mathematics and Computation 79 Ergodic Theory and Dynamical Systems 79 Bulletin of the American Mathematical Society 75 Topology and its Applications 66 Inventiones Mathematicae 64 Communications in Mathematical Physics 63 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 58 Chaos 58 Foundations of Computational Mathematics 57 Chaos, Solitons and Fractals 57 Bulletin of the American Mathematical Society. New Series 55 Journal of Computational and Applied Mathematics 53 Advances in Mathematics 51 Journal of Mathematical Sciences (New York) 48 Mathematische Zeitschrift 45 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 44 Automatica 44 Journal of Economic Theory 42 Journal of Statistical Physics 40 Computers & Mathematics with Applications 39 Journal of Mathematical Physics 39 Mathematische Annalen 38 Archive for Rational Mechanics and Analysis 37 Mathematical Notes 37 Journal of Dynamics and Differential Equations 37 Nonlinear Analysis. Theory, Methods & Applications 35 Journal of Mathematical Biology 35 Linear Algebra and its Applications 35 Analysis and Applications (Singapore) 34 Journal of Symbolic Computation 33 Neural Computation 33 Celestial Mechanics and Dynamical Astronomy 33 Discrete and Continuous Dynamical Systems 31 Journal of Optimization Theory and Applications 30 Discrete & Computational Geometry 30 Applied and Computational Harmonic Analysis 28 Communications in Nonlinear Science and Numerical Simulation 27 Mathematics of Computation 27 Bulletin of Mathematical Biology 27 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 26 Journal of Geometry and Physics 26 Abstract and Applied Analysis 26 Geometry & Topology 26 Qualitative Theory of Dynamical Systems 25 Publications Mathématiques 25 Journal of Functional Analysis 25 Journal of Economic Dynamics & Control 25 Advances in Computational Mathematics 24 Mathematical Biosciences 24 Applied Mathematics Letters 24 Regular and Chaotic Dynamics 24 International Journal of Wavelets, Multiresolution and Information Processing 24 Proceedings of the Steklov Institute of Mathematics 23 Israel Journal of Mathematics 23 Journal of the Franklin Institute 23 Systems & Control Letters 23 Nonlinear Analysis. Real World Applications 22 Duke Mathematical Journal 22 Mathematical Programming. Series A. Series B 21 Nonlinearity 21 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 21 Journal of Approximation Theory 21 Mathematical Programming 21 Acta Applicandae Mathematicae 21 Celestial Mechanics 21 SIAM Journal on Applied Dynamical Systems 20 Annales de l’Institut Fourier 20 Geometriae Dedicata 20 Journal of Nonlinear Science 20 Journal of Difference Equations and Applications 20 Nonlinear Dynamics 19 The Annals of Statistics 17 Neural Networks 17 Algebraic & Geometric Topology 17 Journal of Theoretical Biology 16 Journal of Pure and Applied Algebra 16 Mathematical Problems in Engineering 16 Differential Equations 16 Journal of Fixed Point Theory and Applications 16 Kinetic and Related Models 16 Science China. Mathematics 15 Computer Methods in Applied Mechanics and Engineering 15 General Relativity and Gravitation 15 Physics Letters. A 15 Annali di Matematica Pura ed Applicata. Serie Quarta 15 Annals of Global Analysis and Geometry 15 Constructive Approximation 15 Journal of the American Mathematical Society 15 Mathematical and Computer Modelling 15 Economic Theory 14 ZAMP. Zeitschrift für angewandte Mathematik und Physik ...and 566 more Serials
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#### Cited in 63 Fields

 1,734 Dynamical systems and ergodic theory (37-XX) 914 Computer science (68-XX) 811 Ordinary differential equations (34-XX) 677 Numerical analysis (65-XX) 525 Manifolds and cell complexes (57-XX) 461 Biology and other natural sciences (92-XX) 448 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 446 Global analysis, analysis on manifolds (58-XX) 416 Partial differential equations (35-XX) 379 Differential geometry (53-XX) 379 Mechanics of particles and systems (70-XX) 331 Operations research, mathematical programming (90-XX) 321 Statistics (62-XX) 301 Systems theory; control (93-XX) 241 Probability theory and stochastic processes (60-XX) 205 Algebraic topology (55-XX) 188 Operator theory (47-XX) 175 Calculus of variations and optimal control; optimization (49-XX) 174 General topology (54-XX) 160 Algebraic geometry (14-XX) 157 Statistical mechanics, structure of matter (82-XX) 154 Functions of a complex variable (30-XX) 152 Mathematical logic and foundations (03-XX) 150 Functional analysis (46-XX) 137 Information and communication theory, circuits (94-XX) 136 Fluid mechanics (76-XX) 99 Linear and multilinear algebra; matrix theory (15-XX) 97 Several complex variables and analytic spaces (32-XX) 95 Real functions (26-XX) 94 Field theory and polynomials (12-XX) 90 Measure and integration (28-XX) 89 Approximations and expansions (41-XX) 87 Combinatorics (05-XX) 79 Quantum theory (81-XX) 63 Number theory (11-XX) 60 Harmonic analysis on Euclidean spaces (42-XX) 58 Difference and functional equations (39-XX) 57 Convex and discrete geometry (52-XX) 55 History and biography (01-XX) 55 Mechanics of deformable solids (74-XX) 42 Commutative algebra (13-XX) 42 Relativity and gravitational theory (83-XX) 41 Group theory and generalizations (20-XX) 38 Topological groups, Lie groups (22-XX) 34 General and overarching topics; collections (00-XX) 33 Integral equations (45-XX) 25 Potential theory (31-XX) 17 Optics, electromagnetic theory (78-XX) 17 Geophysics (86-XX) 16 Nonassociative rings and algebras (17-XX) 14 Geometry (51-XX) 13 $$K$$-theory (19-XX) 12 Category theory; homological algebra (18-XX) 12 Special functions (33-XX) 12 Classical thermodynamics, heat transfer (80-XX) 11 Astronomy and astrophysics (85-XX) 10 Abstract harmonic analysis (43-XX) 8 Order, lattices, ordered algebraic structures (06-XX) 6 Associative rings and algebras (16-XX) 6 Integral transforms, operational calculus (44-XX) 3 Mathematics education (97-XX) 1 General algebraic systems (08-XX) 1 Sequences, series, summability (40-XX)

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