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Author ID: smale.steve Recent zbMATH articles by "Smale, Stephen"
Published as: Smale, Steve; Smale, S.; Smale, Stephen; Smale, Steven; Smale, Stephan
Homepage: https://home.ttic.edu/~smale/index.html
External Links: MacTutor · MGP · Wikidata · Google Scholar · Math-Net.Ru · dblp · GND · IdRef
Awards: Fields Medal (1966) · Wolf Prize (2007)
all top 5

Co-Authors

85 single-authored
20 Shub, Michael
13 Cucker, Felipe
10 Zhou, Dingxuan
6 Blum, Lenore
5 Hirsch, Morris W.
4 Rajapakse, Indika
3 Chern, Shiing-Shen
3 Jetter, Kurt
3 Niyogi, Partha
3 Poggio, Tomaso A.
3 Weinberger, Shmuel
2 Caponnetto, Andrea
2 Devaney, Robert L.
2 Lashof, Richard K.
2 Smale, Nathan
1 Abraham, Ralph Herman
1 Baker, Anthony Wayne
1 Bartholdi, Laurent
1 Berry, Michael Victor
1 Bouvrie, Jake
1 Chernoff, Paul R.
1 Childs, Gary
1 Chow, Shui-Nee
1 Christmann, Andreas
1 Coates, John Henry
1 Cohen, Paul Joseph
1 Dedieu, Jean-Pierre
1 Duesberg, Peter
1 Ewing, John Harwood
1 Gerver, Joseph L.
1 Goldberg, Lisa A.
1 Goldfeld, Dorian Morris
1 Greenberg, Marvin Jay
1 Guckenheimer, John M.
1 Guo, Xin
1 Gurdian, Rodolfo
1 Hartwell, Leland Harrison
1 Hirzebruch, Friedrich
1 Howard, Louis N.
1 Howe, Roger Evans
1 Jackson, Allyn
1 Jaffe, Arthur Michael
1 Jorgenson, Jay Alan
1 Karp, Richard Manning
1 Katok, S. B.
1 Khesin, Boris A.
1 Khovanskiĭ, Askold Georgievich
1 Kobayashi, Shoshichi
1 Koiran, Pascal
1 Kopell, Nancy J.
1 Kramer, Jürg
1 Krantz, Steven George
1 Lachaud, Gilles
1 Lanford, Oscar E. III
1 Mallet-Paret, John Joseph
1 Marsden, Jerrold Eldon
1 Mather, John N.
1 Mazur, Barry
1 McCracken, Marjorie F.
1 Mumford, David Bryant
1 Oster, George
1 Palais, Richard S.
1 Palis, Jacob jun.
1 Renegar, James
1 Rohrlich, David E.
1 Rosasco, Lorenzo A.
1 Ruiz, O.
1 Schappacher, Norbert
1 Schecter, Stephen
1 Schick, Thomas
1 Schmidt, Dieter S.
1 Sevryuk, Mikhail Borisovich
1 Shen, Wenjun
1 Stanley, Morgan
1 Tabachnikov, Serge L.
1 Tu, Loring W.
1 Varchenko, Alexander Nikolaevich
1 Vojta, Paul Alan
1 Williams, Robert F.
1 Wong, Hau-San
1 Wu, Hung-Hsi
1 Wüstholz, Gisbert
1 Xiao, Quanwu
1 Yao, Yuan
1 Yau, Shing-Tung
1 Zhou, Ding-Xuan
all top 5

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
5 Notices of the American Mathematical Society
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 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 Applied Mathematical Sciences
1 Lectures in Applied Mathematics
1 Pure and Applied Mathematics (Academic Press)
1 Pure and Applied Mathematics (Amsterdam)
1 Mathematical Medley
1 Japanese Journal of Mathematics. 3rd Series

Publications by Year

Citations contained in zbMATH Open

143 Publications have been cited 10,567 times in 7,880 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
743
1974
The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale. Zbl 0346.58007
Marsden, J. E.; McCracken, M.
636
1976
Emergent behavior in flocks. Zbl 1366.91116
Cucker, Felipe; Smale, Steve
636
2007
On the mathematical foundations of learning. Zbl 0983.68162
Cucker, Felipe; Smale, Steve
463
2002
Mathematical problems for the next century. Zbl 0947.01011
Smale, Steve
415
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
334
1989
An infinite dimensional version of Sard’s theorem. Zbl 0143.35301
Smale, S.
273
1965
Learning theory estimates via integral operators and their approximations. Zbl 1127.68088
Smale, Steve; Zhou, Ding-Xuan
247
2007
On the mathematics of emergence. Zbl 1166.92323
Cucker, Felipe; Smale, Steve
223
2007
Differential equations, dynamical systems, and an introduction to chaos. 2nd ed. Zbl 1135.37002
Hirsch, Morris W.; Smale, Stephen; Devaney, Robert L.
198
2004
Complexity and real computation: A manifesto. Zbl 0872.68036
Blum, Lenore; Cucker, Felipe; Shub, Mike; Smale, Steve
180
1996
Finding the homology of submanifolds with high confidence from random samples. Zbl 1148.68048
Niyogi, Partha; Smale, Stephen; Weinberger, Shmuel
177
2008
Diffeomorphisms with many periodic points. Zbl 0142.41103
Smale, S.
175
1965
Topology and mechanics. II: The planar \(n\)-body problem. Zbl 0203.26102
Smale, S.
168
1970
Newton’s method estimates from data at one point. Zbl 0613.65058
Smale, Steve
168
1986
Structural stability theorems. Zbl 0214.50702
Palis, J.; Smale, S.
158
1970
The fundamental theorem of algebra and complexity theory. Zbl 0456.12012
Smale, Steve
158
1981
Generalized Poincaré’s conjecture in dimensions greater than four. Zbl 0099.39202
Smale, Stephen
152
1961
Topology and mechanics. I. Zbl 0202.23201
Smale, S.
147
1970
Diffeomorphisms of the 2-sphere. Zbl 0118.39103
Smale, S.
137
1959
On the efficiency of algorithms of analysis. Zbl 0592.65032
Smale, Steve
132
1985
On gradient dynamical systems. Zbl 0136.43702
Smale, S.
126
1961
On the structure of manifolds. Zbl 0109.41103
Smale, S.
125
1962
Shannon sampling and function reconstruction from point values. Zbl 1107.94007
Smale, Steve; Zhou, Ding-Xuan
123
2004
Complexity of Bezout’s theorem. I: Geometric aspects. Zbl 0821.65035
Shub, Michael; Smale, Steve
118
1993
A convergent process of price adjustment and global Newton methods. Zbl 0354.90018
Smale, Steve
113
1976
Estimating the approximation error in learning theory. Zbl 1079.68089
Smale, Steve; Zhou, Ding-Xuan
113
2003
A generalized Morse theory. Zbl 0119.09201
Palais, R. S.; Smale, S.
111
1964
Complexity of Bezout’s theorem. II: Volumes and probabilities. Zbl 0851.65031
Shub, M.; Smale, S.
108
1993
Differential equations, dynamical systems, and an introduction to chaos. 3rd ed. Zbl 1239.37001
Hirsch, Morris W.; Smale, Stephen; Devaney, Robert L.
104
2013
The classification of immersions of spheres in Euclidean spaces. Zbl 0089.18201
Smale, Stephen
103
1959
Shannon sampling. II: Connections to learning theory. Zbl 1107.94008
Smale, Steve; Zhou, Ding-Xuan
99
2005
On the differential equations of species in competition. Zbl 0344.92009
Smale, S.
96
1976
Best choices for regularization parameters in learning theory: on the bias-variance problem. Zbl 1057.68085
Cucker, Felipe; Smale, Steve
94
2002
Morse inequalities for a dynamical system. Zbl 0100.29701
Smale, Stephen
92
1960
Complexity of Bezout’s theorem. III: Condition number and packing. Zbl 0846.65018
Shub, Michael; Smale, Steve
81
1993
Complexity of Bezout’s theorem. IV: Probability of success; extensions. Zbl 0843.65035
Shub, Michael; Smale, Steve
81
1996
Mathematical problems for the next century. Zbl 1031.00005
Smale, Steve
78
2000
Online learning with Markov sampling. Zbl 1170.68022
Smale, Steve; Zhou, Ding-Xuan
77
2009
On the structure of 5-manifolds. Zbl 0101.16103
Smale, Stephen
75
1962
Complexity and real computation. Foreword by Richard M. Karp. Zbl 0948.68068
Blum, Leonore; Cucker, Felipe; Shub, Michael; Smale, Steve
67
1997
Complexity of Bezout’s theorem. V: Polynomial time. Zbl 0846.65022
Shub, M.; Smale, S.
62
1994
The mathematics of learning: dealing with data. Zbl 1083.68100
Poggio, Tomaso; Smale, Steve
62
2003
On the Morse index theorem. Zbl 0166.36102
Smale, S.
58
1965
Algorithms for solving equations. Zbl 0665.65058
Smale, Steve
57
1987
Stable manifolds for differential equations and diffeomorphisms. Zbl 0113.29702
Smale, S.
55
1963
A Vietoris mapping theorem for homotopy. Zbl 0089.39003
Smale, Stephen
52
1957
Complexity theory and numerical analysis. Zbl 0883.65125
Smale, Steve
52
1997
On the average number of steps of the simplex method of linear programming. Zbl 0526.90060
Smale, Steve
50
1983
Morse theory and a non-linear generalization of the Dirichlet problem. Zbl 0131.32305
Smale, S.
47
1964
Global analysis and economics. II: Extension of a theorem of Debreu. Zbl 0316.90006
Smale, S.
47
1974
A topological view of unsupervised learning from noisy data. Zbl 1230.62085
Niyogi, P.; Smale, S.; Weinberger, S.
47
2011
Structurally stable systems are not dense. Zbl 0149.20001
Smale, S.
46
1966
Nongenericity of \(\Omega\)-stability. Zbl 0215.25102
Abraham, R.; Smale, S.
46
1970
Computational complexity: On the geometry of polynomials and a theory of cost. II. Zbl 0625.65036
Shub, M.; Smale, S.
41
1986
Online learning algorithms. Zbl 1119.68098
Smale, Steve; Yao, Yuan
41
2006
Global analysis and economics. VI: Geometric analysis of Pareto optima and price equilibria under classical hypotheses. Zbl 0348.90017
Smale, S.
40
1976
On the mathematical foundations of electrical circuit theory. Zbl 0286.34071
Smale, S.
39
1972
On algorithms for solving f(x)=0. Zbl 0408.65032
Hirsch, Morris W.; Smale, Stephen
39
1979
The mathematics of time. Essays on dynamical systems, economic processes, and related topics. Zbl 0451.58001
Smale, Steve
39
1980
The prisoner’s dilemma and dynamical systems associated to non- cooperative games. Zbl 0463.90099
Smale, Steve
39
1980
Global analysis and economics. V: Pareto theory with constraints. Zbl 0357.90010
Smale, S.
38
1974
Dynamics retrospective: Great problems, attempts that failed. Zbl 0745.58018
Smale, Steve
37
1991
A classification of immersions of the two-sphere. Zbl 0089.18102
Smale, Stephen
34
1959
On the topology of algorithms. I. Zbl 0639.68042
Smale, Steve
31
1987
Geometry on probability spaces. Zbl 1187.68270
Smale, Steve; Zhou, Ding-Xuan
31
2009
Global analysis and economics. III: Pareto Optima and price equilibria. Zbl 0316.90007
Smale, S.
30
1974
Global analysis and economics. I: Pareto optimum and a generalization of Morse theory. Zbl 0269.58009
Smale, Steve
30
1973
Finding a horseshoe on the beaches of Rio. Zbl 0983.37001
Smale, Steve
29
1998
The \(\Omega\)-stability theorem. Zbl 0205.54104
Smale, S.
28
1970
On the geometry of polynomials and a theory of cost. I. Zbl 0603.65027
Shub, Mike; Smale, Steve
28
1985
A mathematical model of two cells via Turing’s equation. Zbl 0333.92002
Smale, S.
27
1974
Notes on differentiable dynamical systems. Zbl 0205.54201
Smale, S.
27
1970
Regular curves on Riemannian manifolds. Zbl 0081.38103
Smale, Stephen
27
1958
Modeling language evolution. Zbl 1083.68131
Cucker, Felipe; Smale, Steve; Zhou, Ding-Xuan
26
2004
Global analysis and economics. IV: Finiteness and stability of equilibria with general consumption sets and production. Zbl 0316.90008
Smale, S.
25
1974
On the immersion of manifolds in Euclidean space. Zbl 0097.38805
Lashof, R.; Smale, S.
25
1958
The qualitative analysis of a difference equation of population growth. Zbl 0342.92014
Smale, S.; Williams, R. F.
24
1976
Exchange processes with price adjustment. Zbl 0366.90013
Smale, Stephen
22
1976
Complexity estimates depending on condition and round-off error. Zbl 1065.68533
Cucker, Felipe; Smale, Steve
19
1999
On the intractability of Hilbert’s Nullstellensatz and an algebraic version of “\(NP\neq P\)?”. Zbl 0882.03040
Shub, Michael; Smale, Steve
19
1995
The generalized Poincaré conjecture in higher dimensions. Zbl 0099.39201
Smale, Stephen
18
1960
Separation of complexity classes in Koiran’s weak model. Zbl 0819.68053
Cucker, F.; Shub, M.; Smale, S.
15
1994
Beyond hyperbolicity. Zbl 0247.58008
Shub, M.; Smale, S.
15
1972
On the existence of generally convergent algorithms. Zbl 0595.65048
Shub, Michael; Smale, Steve
15
1986
Some remarks on the foundations of numerical analysis. Zbl 0703.65003
Smale, Steve
15
1990
Hodge theory on metric spaces. Appendix by Anthony W. Baker. Zbl 1366.58001
Bartholdi, Laurent; Schick, Thomas; Smale, Nat; Smale, Steve
14
2012
A polynomial time algorithm for diophantine equations in one variable. Zbl 0920.11085
Cucker, Felipe; Koiran, Pascal; Smale, Steve
14
1999
Smooth solutions of the heat and wave equations. Zbl 0439.35017
Smale, Stephen
14
1980
Problems on the nature of relative equilibria in celestial mechanics. Zbl 0215.52602
Smale, S.
13
1971
Self-intersections of immersed manifolds. Zbl 0093.37501
Lashof, R. K.; Smale, S.
13
1959
The problem of the average speed of the simplex method. Zbl 0552.90059
Smale, S.
13
1983
Optimizing several functions. Zbl 0349.90086
Smale, Stephen
12
1975
On the problem of reviving the ergodic hypothesis of Boltzmann and Birkhoff. Zbl 0486.58014
Smale, S.
12
1980
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.
12
1990
Global analysis and economics. Zbl 0477.90014
Smale, Steve
12
1981
Global analysis and economics. I: Pareto optimum and a generalisation of Morse theory. Zbl 0267.58008
Smale, S.
11
1972
Algebraic settings for the problem ”P\(\neq\)NP?”. Zbl 0856.68068
Blum, Lenore; Cucker, Felipe; Shub, Mike; Smale, Steve
11
1996
On dynamical systems. Zbl 0121.17906
Smale, S.
10
1960
Mathematics of the genome. Zbl 1380.37148
Rajapakse, Indika; Smale, Steve
6
2017
Emergence of function from coordinated cells in a tissue. Zbl 1404.92067
Rajapakse, Indika; Smale, Stephen
5
2017
The pitchfork bifurcation. Zbl 1373.34058
Rajapakse, Indika; Smale, Steve
4
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
5
2014
Differential equations, dynamical systems, and an introduction to chaos. 3rd ed. Zbl 1239.37001
Hirsch, Morris W.; Smale, Stephen; Devaney, Robert L.
104
2013
Hodge theory on metric spaces. Appendix by Anthony W. Baker. Zbl 1366.58001
Bartholdi, Laurent; Schick, Thomas; Smale, Nat; Smale, Steve
14
2012
Abstract and classical Hodge-de Rham theory. Zbl 1243.58003
Smale, Nat; Smale, Steve
4
2012
A topological view of unsupervised learning from noisy data. Zbl 1230.62085
Niyogi, P.; Smale, S.; Weinberger, S.
47
2011
Mathematics of the neural response. Zbl 1185.68813
Smale, S.; Rosasco, L.; Bouvrie, J.; Caponnetto, A.; Poggio, T.
7
2010
Online learning with Markov sampling. Zbl 1170.68022
Smale, Steve; Zhou, Ding-Xuan
77
2009
Geometry on probability spaces. Zbl 1187.68270
Smale, Steve; Zhou, Ding-Xuan
31
2009
Finding the homology of submanifolds with high confidence from random samples. Reprinted from the journal Discrete & Computational Geometry 39, No. 1-3 (2008). Zbl 1177.62003
Niyogi, Partha; Smale, Stephen; Weinberger, Shmuel
6
2009
Finding the homology of submanifolds with high confidence from random samples. Zbl 1148.68048
Niyogi, Partha; Smale, Stephen; Weinberger, Shmuel
177
2008
Learning theory and approximation. Abstracts from the workshop held June 29 – July 5, 2008. Zbl 1177.68114
1
2008
Emergent behavior in flocks. Zbl 1366.91116
Cucker, Felipe; Smale, Steve
636
2007
Learning theory estimates via integral operators and their approximations. Zbl 1127.68088
Smale, Steve; Zhou, Ding-Xuan
247
2007
On the mathematics of emergence. Zbl 1166.92323
Cucker, Felipe; Smale, Steve
223
2007
Risk bounds for random regression graphs. Zbl 1368.68278
Caponnetto, A.; Smale, S.
4
2007
Online learning algorithms. Zbl 1119.68098
Smale, Steve; Yao, Yuan
41
2006
Shannon sampling. II: Connections to learning theory. Zbl 1107.94008
Smale, Steve; Zhou, Ding-Xuan
99
2005
The mathematics of learning: dealing with data. Zbl 1083.68589
Poggio, T.; Smale, S.
1
2005
On problems of computational complexity. Zbl 1147.68527
Smale, Stephen
1
2005
Differential equations, dynamical systems, and an introduction to chaos. 2nd ed. Zbl 1135.37002
Hirsch, Morris W.; Smale, Stephen; Devaney, Robert L.
198
2004
Shannon sampling and function reconstruction from point values. Zbl 1107.94007
Smale, Steve; Zhou, Ding-Xuan
123
2004
Modeling language evolution. Zbl 1083.68131
Cucker, Felipe; Smale, Steve; Zhou, Ding-Xuan
26
2004
Estimating the approximation error in learning theory. Zbl 1079.68089
Smale, Steve; Zhou, Ding-Xuan
113
2003
The mathematics of learning: dealing with data. Zbl 1083.68100
Poggio, Tomaso; Smale, Steve
62
2003
On the mathematical foundations of learning. Zbl 0983.68162
Cucker, Felipe; Smale, Steve
463
2002
Best choices for regularization parameters in learning theory: on the bias-variance problem. Zbl 1057.68085
Cucker, Felipe; Smale, Steve
94
2002
Mathematical problems for the next century. Zbl 1031.00005
Smale, Steve
78
2000
The collected papers of Stephen Smale. Vols. 1-3. Edited by F. Cucker and R. Wong. Zbl 0995.01005
Smale, Stephen
9
2000
Mathematical problems of the next century. Zbl 1077.01502
Smale, S.
6
2000
Finding a horseshoe on the beaches of Rio. Zbl 0983.37002
Smale, Steve
2
2000
On how I got started in dynamical systems 1959-1962. Zbl 0983.37003
Smale, Steve
1
2000
Mathematical problems for the next century. (Problèmes mathématiques pour le prochain siècle.) Zbl 1040.01006
Smale, Steve
1
2000
Complexity estimates depending on condition and round-off error. Zbl 1065.68533
Cucker, Felipe; Smale, Steve
19
1999
A polynomial time algorithm for diophantine equations in one variable. Zbl 0920.11085
Cucker, Felipe; Koiran, Pascal; Smale, Steve
14
1999
Mathematical problems for the next century. Zbl 0947.01011
Smale, Steve
415
1998
Finding a horseshoe on the beaches of Rio. Zbl 0983.37001
Smale, Steve
29
1998
Some lower bounds for the complexity of continuation methods. Zbl 0918.65038
Dedieu, Jean-Pierre; Smale, Steve
2
1998
Complexity estimates depending on condition and round-of error. Zbl 0929.65027
Cucker, Felipe; Smale, Steve
1
1998
The work of Curtis T. McMullen. Zbl 1288.01063
Smale, Steven
1
1998
Complexity and real computation. Foreword by Richard M. Karp. Zbl 0948.68068
Blum, Leonore; Cucker, Felipe; Shub, Michael; Smale, Steve
67
1997
Complexity theory and numerical analysis. Zbl 0883.65125
Smale, Steve
52
1997
Complexity and real computation: A manifesto. Zbl 0872.68036
Blum, Lenore; Cucker, Felipe; Shub, Mike; Smale, Steve
180
1996
Complexity of Bezout’s theorem. IV: Probability of success; extensions. Zbl 0843.65035
Shub, Michael; Smale, Steve
81
1996
Algebraic settings for the problem ”P\(\neq\)NP?”. Zbl 0856.68068
Blum, Lenore; Cucker, Felipe; Shub, Mike; Smale, Steve
11
1996
The mathematics of numerical analysis. 1995 AMS-SIAM summer seminar in applied mathematics, July 17–August 11, 1995, Park City, UT, USA. Zbl 0852.00035
2
1996
On the intractability of Hilbert’s Nullstellensatz and an algebraic version of “\(NP\neq P\)?”. Zbl 0882.03040
Shub, Michael; Smale, Steve
19
1995
Complexity of Bezout’s theorem. V: Polynomial time. Zbl 0846.65022
Shub, M.; Smale, S.
62
1994
Separation of complexity classes in Koiran’s weak model. Zbl 0819.68053
Cucker, F.; Shub, M.; Smale, S.
15
1994
Complexity of Bezout’s theorem. I: Geometric aspects. Zbl 0821.65035
Shub, Michael; Smale, Steve
118
1993
Complexity of Bezout’s theorem. II: Volumes and probabilities. Zbl 0851.65031
Shub, M.; Smale, S.
108
1993
Complexity of Bezout’s theorem. III: Condition number and packing. Zbl 0846.65018
Shub, Michael; Smale, Steve
81
1993
The Gödel incompleteness theorem and decidability over a ring. Zbl 0793.03066
Blum, Lenore; Smale, Steve
6
1993
Dynamics retrospective: Great problems, attempts that failed. Zbl 0745.58018
Smale, Steve
37
1991
Some remarks on the foundations of numerical analysis. Zbl 0703.65003
Smale, Steve
15
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.
12
1990
The story of the higher dimensional Poincaré conjecture (what actually happened on the beaches of Rio). Zbl 0703.57001
Smale, Steve
4
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
334
1989
Algorithms for solving equations. Zbl 0665.65058
Smale, Steve
57
1987
On the topology of algorithms. I. Zbl 0639.68042
Smale, Steve
31
1987
Newton’s method estimates from data at one point. Zbl 0613.65058
Smale, Steve
168
1986
Computational complexity: On the geometry of polynomials and a theory of cost. II. Zbl 0625.65036
Shub, M.; Smale, S.
41
1986
On the existence of generally convergent algorithms. Zbl 0595.65048
Shub, Michael; Smale, Steve
15
1986
On the efficiency of algorithms of analysis. Zbl 0592.65032
Smale, Steve
132
1985
On the geometry of polynomials and a theory of cost. I. Zbl 0603.65027
Shub, Mike; Smale, Steve
28
1985
On the average number of steps of the simplex method of linear programming. Zbl 0526.90060
Smale, Steve
50
1983
The problem of the average speed of the simplex method. Zbl 0552.90059
Smale, S.
13
1983
On the average cost of solving polynomial equations. Zbl 0529.41008
Shub, Mike; Smale, Steve
2
1983
The fundamental theorem of algebra and complexity theory. Zbl 0456.12012
Smale, Steve
158
1981
Global analysis and economics. Zbl 0477.90014
Smale, Steve
12
1981
The mathematics of time. Essays on dynamical systems, economic processes, and related topics. Zbl 0451.58001
Smale, Steve
39
1980
The prisoner’s dilemma and dynamical systems associated to non- cooperative games. Zbl 0463.90099
Smale, Steve
39
1980
Smooth solutions of the heat and wave equations. Zbl 0439.35017
Smale, Stephen
14
1980
On the problem of reviving the ergodic hypothesis of Boltzmann and Birkhoff. Zbl 0486.58014
Smale, S.
12
1980
On algorithms for solving f(x)=0. Zbl 0408.65032
Hirsch, Morris W.; Smale, Stephen
39
1979
On comparative statics and bifurcation in economic equilibrium theory. Zbl 0437.90026
Smale, Steve
1
1979
An approach to the analysis of dynamic processes in economic systems. Zbl 0387.90031
Smale, Steve
4
1978
Dynamical systems and turbulence. Zbl 0362.58012
Smale, Steve
3
1977
Convergent process of price adjustment and global Newton methods. Zbl 0384.34025
Smale, Steve
2
1977
The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale. Zbl 0346.58007
Marsden, J. E.; McCracken, M.
636
1976
A convergent process of price adjustment and global Newton methods. Zbl 0354.90018
Smale, Steve
113
1976
On the differential equations of species in competition. Zbl 0344.92009
Smale, S.
96
1976
Global analysis and economics. VI: Geometric analysis of Pareto optima and price equilibria under classical hypotheses. Zbl 0348.90017
Smale, S.
40
1976
The qualitative analysis of a difference equation of population growth. Zbl 0342.92014
Smale, S.; Williams, R. F.
24
1976
Exchange processes with price adjustment. Zbl 0366.90013
Smale, Stephen
22
1976
Optimizing several functions. Zbl 0349.90086
Smale, Stephen
12
1975
Sufficient conditions for an optimum. Zbl 0314.58007
Smale, S.
8
1975
Global analysis and economics. Pareto optimum and a generalization of Morse theory. Zbl 0312.90007
Smale, Steve
6
1975
Differential equations, dynamical systems, and linear algebra. Zbl 0309.34001
Hirsch, Morris W.; Smale, Stephen
743
1974
Global analysis and economics. II: Extension of a theorem of Debreu. Zbl 0316.90006
Smale, S.
47
1974
Global analysis and economics. V: Pareto theory with constraints. Zbl 0357.90010
Smale, S.
38
1974
Global analysis and economics. III: Pareto Optima and price equilibria. Zbl 0316.90007
Smale, S.
30
1974
A mathematical model of two cells via Turing’s equation. Zbl 0333.92002
Smale, S.
27
1974
Global analysis and economics. IV: Finiteness and stability of equilibria with general consumption sets and production. Zbl 0316.90008
Smale, S.
25
1974
Global analysis and economics. I: Pareto optimum and a generalization of Morse theory. Zbl 0269.58009
Smale, Steve
30
1973
Stability and isotopy in discrete dynamical systems. Zbl 0284.58013
Smale, Steve
4
1973
On the mathematical foundations of electrical circuit theory. Zbl 0286.34071
Smale, S.
39
1972
Beyond hyperbolicity. Zbl 0247.58008
Shub, M.; Smale, S.
15
1972
...and 43 more Documents
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Cited by 8,682 Authors

109 Ha, Seung-Yeal
70 Grines, Vyacheslav Zigmundovich
63 Llibre, Jaume
60 Pochinka, Ol’ga Vital’evna
58 Zhou, Dingxuan
48 Cucker, Felipe
42 Smale, Stephen
34 Choi, Young-Pil
34 Shub, Michael
33 Medvedev, Vladislav Sergeevich
32 Carrillo de la Plata, José Antonio
30 Zhuzhoma, Evgeniĭ Viktorovich
27 Kim, Jeongho
26 Beltrán, Carlos E.
26 Liu, Yicheng
25 Marsden, Jerrold Eldon
25 Sheng, Baohuai
24 Koiran, Pascal
24 Petković, Miodrag S.
24 Sun, Hongwei
24 Yu, Pei
23 Chen, Dirong
23 Degond, Pierre
23 Meer, Klaus
22 Bonatti, Christian
21 Bürgisser, Peter
21 Jørgensen, Palle E. T.
21 Yorke, James Alan
20 Argyros, Ioannis Konstantinos
20 Han, Maoan
20 Mello, Luis Fernando O.
20 Pardo, Luis Miguel
20 Pillonetto, Gianluigi
19 Gurevich, Elena Ya.
19 Hirsch, Morris W.
19 Holmes, Philip J.
19 Shi, Lei
18 Guo, Zheng-Chu
18 Hu, Ting
18 Xiang, Dao-Hong
17 Rosasco, Lorenzo A.
17 Ruelle, David Pierre
17 Wu, Qiang
17 Zhang, Xiongtao
16 Basu, Saugata
16 Fernandes, Antonio Carlos
16 Ko, Dongnam
16 Laudenbach, François
16 Li, Chong
16 Shim, Woojoo
16 Tan, Changhui
16 Tong, Hongzhi
15 Dong, Jiu-Gang
15 Fornasier, Massimo
15 Graça, Daniel Silva
15 Jin, Shi
15 Kim, Doheon
15 Kim, Dohyun
15 Kuznetsov, Sergey P.
15 Li, Luoqing
15 Tadmor, Eitan
15 Xu, Zongben
15 Yang, Qigui
15 Zou, Bin
14 Ahn, Hyunjin
14 Bellomo, Nicola
14 Shvydkoy, Roman V.
14 Wang, Cheng
13 Chen, Guanrong
13 Chen, Hong
13 Crovisier, Sylvain
13 Malajovich, Gregorio
13 Palis, Jacob jun.
13 Xie, Zhifu
13 Zanolin, Fabio
12 De Vito, Ernesto
12 Dedieu, Jean-Pierre
12 Ferreira, Orizon Pereira
12 Gan, Shaobo
12 Haskovec, Jan
12 Lee, Manseob
12 Lerario, Antonio
12 Li, Jibin
12 Lin, Shaobo
12 Pérez-Chavela, Ernesto
12 Rančić, Lidija Z.
12 Rojas, J. Maurice
12 Sanguineti, Marcello
12 Xian, Jun
12 Xue, Xiaoping
12 Zhang, Haizhang
12 Zhong, Ning
11 Armentano, Diego
11 Bournez, Olivier
11 Chazal, Frédéric
11 Devaney, Robert L.
11 Guckenheimer, John M.
11 Li, Zhuchun
11 Pugh, Charles Chapman
11 Santoprete, Manuele
...and 8,582 more Authors
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Cited in 813 Serials

234 Journal of Differential Equations
187 Transactions of the American Mathematical Society
170 Journal of Complexity
148 Physica D
142 Journal of Mathematical Analysis and Applications
134 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
118 Proceedings of the American Mathematical Society
102 Theoretical Computer Science
99 Ergodic Theory and Dynamical Systems
95 Journal of Mathematical Economics
92 Applied Mathematics and Computation
82 Topology and its Applications
81 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
79 Bulletin of the American Mathematical Society
74 Chaos, Solitons and Fractals
72 Inventiones Mathematicae
71 Communications in Mathematical Physics
70 Foundations of Computational Mathematics
62 Advances in Mathematics
61 Journal of Computational and Applied Mathematics
61 Chaos
60 Bulletin of the American Mathematical Society. New Series
57 Journal of Mathematical Sciences (New York)
56 Journal of Mathematical Physics
56 Mathematische Zeitschrift
55 Automatica
52 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
52 Discrete and Continuous Dynamical Systems
49 Journal of Statistical Physics
49 Journal of Dynamics and Differential Equations
49 Communications in Nonlinear Science and Numerical Simulation
46 Applied and Computational Harmonic Analysis
44 Journal of Economic Theory
44 Mathematische Annalen
44 Discrete & Computational Geometry
43 Computers & Mathematics with Applications
43 Mathematical Notes
43 Nonlinearity
42 Archive for Rational Mechanics and Analysis
42 Journal of Symbolic Computation
42 Analysis and Applications (Singapore)
41 Journal of Mathematical Biology
41 SIAM Journal on Applied Dynamical Systems
39 Celestial Mechanics and Dynamical Astronomy
37 Journal of Optimization Theory and Applications
37 Nonlinear Analysis. Theory, Methods & Applications
36 Linear Algebra and its Applications
36 Geometry & Topology
36 Regular and Chaotic Dynamics
35 Qualitative Theory of Dynamical Systems
34 Neural Computation
32 Kinetic and Related Models
31 Mathematical Biosciences
31 Mathematics of Computation
31 Journal of Machine Learning Research (JMLR)
31 International Journal of Wavelets, Multiresolution and Information Processing
29 Physics Letters. A
29 Advances in Computational Mathematics
29 Discrete and Continuous Dynamical Systems. Series B
28 Journal of Geometry and Physics
28 Journal of Functional Analysis
28 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
28 Applied Mathematics Letters
27 Bulletin of Mathematical Biology
27 Duke Mathematical Journal
27 Nonlinear Dynamics
27 Proceedings of the Steklov Institute of Mathematics
26 Publications Mathématiques
26 Journal of Approximation Theory
26 Journal of Economic Dynamics & Control
26 Mathematical Programming. Series A. Series B
25 Geometriae Dedicata
25 Systems & Control Letters
25 Acta Applicandae Mathematicae
25 Abstract and Applied Analysis
25 Nonlinear Analysis. Real World Applications
25 Algebraic & Geometric Topology
24 The Annals of Statistics
24 SIAM Journal on Mathematical Analysis
24 Journal of Nonlinear Science
24 Journal of Difference Equations and Applications
24 Journal of Theoretical Biology
23 Journal of the Franklin Institute
23 Physica A
23 Neural Networks
22 Annales de l’Institut Fourier
22 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
21 Israel Journal of Mathematics
21 Mathematical Programming
21 Numerical Algorithms
21 Celestial Mechanics
21 Science China. Mathematics
20 SIAM Journal on Control and Optimization
20 Constructive Approximation
20 Machine Learning
20 Communications on Pure and Applied Analysis
19 Applicable Analysis
19 Annals of Global Analysis and Geometry
19 Bulletin of the Brazilian Mathematical Society. New Series
19 Journal of Fixed Point Theory and Applications
...and 713 more Serials
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Cited in 63 Fields

2,191 Dynamical systems and ergodic theory (37-XX)
1,124 Computer science (68-XX)
1,035 Ordinary differential equations (34-XX)
855 Numerical analysis (65-XX)
665 Biology and other natural sciences (92-XX)
660 Manifolds and cell complexes (57-XX)
607 Partial differential equations (35-XX)
532 Global analysis, analysis on manifolds (58-XX)
515 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
512 Differential geometry (53-XX)
492 Mechanics of particles and systems (70-XX)
469 Statistics (62-XX)
414 Operations research, mathematical programming (90-XX)
391 Systems theory; control (93-XX)
352 Probability theory and stochastic processes (60-XX)
293 Algebraic topology (55-XX)
257 Operator theory (47-XX)
247 Statistical mechanics, structure of matter (82-XX)
237 Calculus of variations and optimal control; optimization (49-XX)
225 Functional analysis (46-XX)
221 Algebraic geometry (14-XX)
198 Fluid mechanics (76-XX)
189 General topology (54-XX)
176 Functions of a complex variable (30-XX)
172 Mathematical logic and foundations (03-XX)
168 Information and communication theory, circuits (94-XX)
138 Approximations and expansions (41-XX)
131 Several complex variables and analytic spaces (32-XX)
130 Combinatorics (05-XX)
124 Linear and multilinear algebra; matrix theory (15-XX)
116 Quantum theory (81-XX)
114 Real functions (26-XX)
104 Measure and integration (28-XX)
102 Field theory and polynomials (12-XX)
84 Harmonic analysis on Euclidean spaces (42-XX)
76 Number theory (11-XX)
76 Convex and discrete geometry (52-XX)
70 Difference and functional equations (39-XX)
65 History and biography (01-XX)
65 Mechanics of deformable solids (74-XX)
62 Group theory and generalizations (20-XX)
55 Commutative algebra (13-XX)
50 Topological groups, Lie groups (22-XX)
50 Relativity and gravitational theory (83-XX)
43 Integral equations (45-XX)
41 Potential theory (31-XX)
38 General and overarching topics; collections (00-XX)
24 Nonassociative rings and algebras (17-XX)
24 Optics, electromagnetic theory (78-XX)
23 Geophysics (86-XX)
21 Category theory; homological algebra (18-XX)
20 Geometry (51-XX)
18 \(K\)-theory (19-XX)
18 Classical thermodynamics, heat transfer (80-XX)
15 Astronomy and astrophysics (85-XX)
14 Special functions (33-XX)
13 Abstract harmonic analysis (43-XX)
10 Order, lattices, ordered algebraic structures (06-XX)
9 Associative rings and algebras (16-XX)
7 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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