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BIBLIOGRAPHY


Steve Smale


1951-60 1961-70 1971-80 


  1981-90   

  1991-2000  














    
  
  1.  A note on open maps,  Proceedings of the AMS,  8 (1957),
pp. 391--393.
   
    

  
  2.  A Vietoris mapping theorem for homotopy,  Proceedings of the
AMS,  8 (1957), pp. 604--610.
   
    

  
  3.  Regular curves on Riemannian manifolds,  Transactions of the
AMS,  87 (1958), pp. 492--512.
   
    

  
  4.  On the immersions of manifolds in Euclidean space (with R. K.
Lashof),  Annals of Mathematics,  68 (1958), pp. 562--583.
   
    

  
  5.  Self-intersections of immersed manifolds (with R. K. Lashof), 
Journal of Mathematics and Mechanics,  8 (1959), pp. 143--157.
   
    

  
  6.  A classification of immersions of the two-sphere,  Transactions of
the AMS,  90 (1959), pp. 281--290.
   
    

  
  7.  The classification of immersions of spheres in Euclidean space, 
Annals of Mathematics,  69 (1959), pp. 327--344.  (See also R. Thom, La
Classification des immersions d'apres Smale,  Seminaire Bourbaki, December
1957.)
   
    

  
  8.  Diffeomorphisms of the two-sphere,  Proceedings of the AMS,  10
(1959), pp. 621--626.
    
    

  
  9.  On involutions of the 3-sphere (with Morris Hirsch),  American
Journal of Mathematics,  81 (1959), pp. 893--900.
    
    

  
  10.  Morse inequalities for a dynamical system,  Bulletin of the AMS,
 66 (1960), pp. 43--49.
    
    

  
  11.  The generalized Poincaré conjecture in higher dimensions,  Bulletin
of the AMS,  66 (1960), pp. 373--375.
    
    

  
  12.  On dynamical systems,  Boletin de la Sociedad Mathematics Mexicana,
(1960), pp. 195--198.
   
    


    

    
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  13.  On gradient dynamical systems,  Annals of Mathematics,  74
(1961), pp. 199--206.
   
    

  
  14.  Generalized Poincaré conjecture in dimensions greater than 4, 
Annals of Mathematics,  74 (1961), pp. 391--406.
   
    

  
  15.  Differentiable and combinatorial structures on manifolds,  Annals of
Mathematics,  74 (1961), pp. 498--502.
   
    

  
  16.  On the structure of 5-manifolds,  Annals of Mathematics,  75
(1962), pp. 38--46.
   
    

  
  17.  On the structure of manifolds,  American Journal of Mathematics,
 84 (1962), pp. 387--399.
   
    

  
  18.  Dynamical systems and the topological conjugacy problem for
diffeomorphisms,  Proceedings of the International Congress of
Mathematicians, Stockholm, 1962.
   
    

  
  19.  A survey of some recent developments in differential topology, 
Bulletin of the AMS,  69 (1963), pp. 131--146.
   
    

  
  20.  Stable manifolds of diffeomorphisms and differential equations, 
Annali della Scuola Normali Superioro di Pisa, Serie III,  XVII (1963),
pp. 97--116.
   
    

  
  21.  A generalized Morse theory (with R. Palais),  Bulletin of the AMS,
 70 (1964), pp. 165--172.
    
    

  
  22.  Morse theory and non-linear generalization of the Dirichlet problem, 
Annals of Mathematics,  80, pp. 382--396.
   
    

  
  23.  Diffeomorphisms with many periodic points,  Differential and
Combinatorial Topology (A symposium in honor of Marston Morse), Princeton
University Press (1965), pp. 63--80.
   
    

  
  24.  An infinite dimensional version of Sard's theorem,  American Journal
of Mathematics,  87 (1965), pp. 861--866.
   
    

  
  25.  On the Morse index theorem,  Journal of Mathematics and Mechanics,
 14 (1965), pp. 1049--1056.
   
    

  
  26.  A structurally stable differentiable homeomorphism with an infinite
number of periodic points,  Report on the Symposium on Non Linear
Oscillations, Kiev Mathematics Institute (1963), pp. 365--366.
   
    

  
  27.  On the calculus of variations,  Differential Analysis, Bombay
(1964), pp. 187--189.
   
    

  
  28.  Structurally stable systems are not dense,  American Journal of
Mathematics,  88 (1966), pp. 491--496.
   
    

  
  29.  Dynamical systems on n-dimensional manifolds,  Differential
Equations and Dynamical Systems, (1967), pp. 483--486.
   
    

  
  30.  Differentiable dynamical systems,  Bulletin of the AMS,  73
(1967), pp. 747--817.
   
    

  
  31.  What is global analysis?,  American Math. Monthly, (1969), pp. 4--9.
   
    

  
  32.  Nongenericity of -stability (with R. Abraham),  Global
Analysis, Proc. of Symposia in Pure Mathematics,  14 AMS (1970), pp. 5--8.
   
    

  
  33.  Structural stability theorems (with J. Palis),  Global Analysis,
Proc. of Symposia in Pure Mathematics,  14 AMS (1970), pp. 223--231.
   
    

  
  34.  Notes on differential dynamical systems,  Global Analysis, Proc. of
Symposia in Pure Mathematics,  14 AMS (1970), pp. 277--287.
   
    

  
  35.  The -stability theorem,  Global Analysis, Proc. of Symposia
in Pure Mathematics,  14 AMS (1970), pp. 289--297.
   
    

  
  36.  Topology and mechanics, I.,  Inventiones Mathematicae,  10
(1970), pp. 305--331.
   
    

  
  37.  Topology and mechanics, II.,  Inventiones Mathematicae,  11
(1970), pp. 45--64.
   
    

  
  38.  Stability and genericity in dynamical systems,  Seminaire Bourbaki,
(1969--70), Springer, Berlin, pp. 177--186.
   
    
  
  
  39.  Problems on the nature of relative equilibria in celestial mechanics,
 Proc. of Conference on Manifolds, Amsterdam (1970), Springer, Berlin, pp.
194--198.
   
    


    

    
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  40.  On the mathematical foundations of electrical circuit theory, 
Journal of Differential Geometry,  7 (1972), pp. 193--210.
   
    

  
  41.  Beyond hyperbolicity (with M. Shub),  Annals of Mathematics, 
96 (1972), pp. 591--597.
   
    

  
  42.  Personal perspectives on mathematics and mechanics,  Statistical
Mechanics:  New Concepts, New Problems, New Applications, edited by Stuart A.
Rice, Karl F. Freed, and John C. Light, Univ. of Chicago Press (1972),
pp. 3--12.
   
    

  
  43.  Stability and isotopy in discrete dynamical systems,  Dynamical
Systems, edited by M. M. Peixoto, Academic Press, New York (1973).
   
    

  
  44.  Global analysis and economics, I:  Pareto Optimum and a
generalization of Morse theory,  Dynamical Systems, edited by M. M.
Peixoto,
Academic Press (1973).
   
    

  
  45.  Global analysis and economics, IIA,  Journal of Mathematical
Economics, First Issue, April 1974, pp. 1--14.
   
    

  
  46.  Global analysis and economics, III:  Pareto Optima and price
equilibria,  Journal of Mathematical Economics,  I (1974), pp.
107--117.
   
    

  
  47.  Global analysis and economics, IV:  Finiteness and stability of
equilibria with general consumption sets and production,  Journal of
Mathematical Economics,  I (1974), pp. 119--127.
   
    

  
  48.  Global analysis and economics, V:  Pareto theory with constraints, 
Journal of Mathematical Economics,  I (1974), pp. 213--221.
   
    

  
  49.  Optimizing several functions,  Manifolds, Tokyo (1973),  Proc.
of the International Conference on Manifolds and Related Topics in Topology,
Tokyo (1973), Univ. of Tokyo Press (1975), pp. 69--75.
   
    

  
  50.  The mathematical model of two cells via Turing's equation,  Lectures
on Mathematics in the Life Sciences,  6 (1974), pp. 17--26.
   
    

  
  51.  Sufficient conditions for an optimum,  Warwick Dynamical Systems
(1974),  Lecture Notes in Mathematics, Springer--Verlag (1975), pp.
287--292.
   
    

  
  52.  Differential equations (with I. M. Singer),  Encyclopedia Britannica
Inc., Fifteenth Edition, (1974), pp. 736--767.
   
    

  
  53.  Dynamics in general equilibrium the theory,  American Economic
Review,  66 (1976), pp. 288--294.
   
    

  
  54.  Global analysis and economics, VI:  Geometric analysis of Parieto Optima
and price equilibria under classical hypotheses,  Journal of Mathematical
Economics,  3 (1976), pp. 1--14.
   
    

  
  55.  The qualitative analysis of a difference equation of population growth
(with R. F. Williams),  Journal of Mathematical Biology,  3 (1976),
PP. 1--4.
   
    

  
  56.  On the differential equations of species in competition,  Journal of
Mathematical Biology,  3 (1976), pp. 5--7.
    
    

  
  57.  A convergent process of price adjustment,  Journal of Mathematical
Economics,  3 (1976), pp. 107--120.
    
    

  
  58.  Exchange processes with price adjustment,  Journal of Mathematical
Economics,  3 (1976), pp. 211--226.
   
    

  
  59.  Global stability questions in dynamical systems,  Proceedings of
Conference on Qualitative Analysis, Washington, DC.
    
    




  
  60.  Dynamical systems and turbulence, Turbulence Seminar:  Berkeley 1976/77,
edited by P. Bernard and T. Ratiu,  Lecture Notes in Mathematics, 
615 (1977), pp. 48--71.
    
    

  
  61.  Some dynamical questions in mathematical economics,  Colloques
Internationaux du Centre National de la Recherche Scientifique, No. 259:
Systemes Dynamiques et Modeles Economiques, (1977).
     
     

  
  62.  An approach to the analysis of dynamic processes in economic systems,
 Equilibrium and disequilibrium in Economic Theory, D. Reidel Publishing
Co., Dordrecht, (1977), pp. 363--367.
   
    

  
  63.  On comparative statics and bifurcation in economic equilibrium theory,
 Annals of the New York Academy of Sciences,  316 (1979),
(Bifurcation Theory in Scientific Disciplines), pp. 545--548.
   
    

  
  64.  On algorithms for solving  (with Morris W. Hirsch), 
Communications on Pure and Applied Mathematics,  55 (1980), pp. 1--12.
   
    

  
  65.  Smooth solutions of the heat and wave equations,  Commentarii
Mathematici Helvetici,  55 (1980), pp. 1--12.
   
    

    

    
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  66.  The fundamental theorem of algebra and complexity theory,  Bulletin
of the American Mathematical Society,  4 (1981), pp. 1--36.
   
    

  
  67.  The prisoner's dilemma and dynamical systems associated to
non-cooperative games,  Econometrica,  48 (1980), pp. 1617--1634.
   
    

  
  68.  Global analysis and economics,  Handbook of Mathematical Economics,
K. J. Arrow and M. D. Intrilligator, North-Holland, Amsterdam,  1 (1981),
pp. 331--370.
    
    

  
  69.  The Mathematics of Time:  Essays on Dynamical Systems, Economic Processes
and Related Topics,  Springer--Verlag, Berlin, (1980), vi + pp. 151.
   
    




  
  70.  The problem of the average speed of the simplex method,  Proceedings
of the XIth International Symposium on Mathematical Programming, edited by
Bachem, Grotschel, and Korte, Springer--Verlag, Berlin, (1983), pp. 530--539.
  
    

  
  71.  On the average number of steps of the simplex method of linear
programming,  Mathematical Programming,  27 (1983), pp. 241--262.
   
    

  
  72.  On the steps of Moscow University,  Mathematical Intelligencer, 
6 (1984), pp. 21--27.
   
    

  
  73.  Gerard Debreu wins the Nobel Prize,  Mathematical Intelligencer,
 6 (1984), pp. 61--62.
   
    

  
  74.  Scientists and the arms race (in German translation),
Natur-Wissenschafter Gegen Atomrustung, edited by Hans-Peter Durr, Hans-Peter
Harjes, Matthias Krech, and Peter Starlinge,  Spiegel--Buch, (1983), pp.
327--334.
   
    

  
  75.  Computational complexity:  On the geometry of polynomials and a theory of
cost, Part I (with Mike Shub),  Annales Scientifiques de l'Ecole Normale
Superieure,  18 (1985), pp. 107--142.
   
    

  
  76.  On the efficiency of algorithms of analysis,  Bulletin of the
American Mathematical Society,  13 (1985), pp. 87--121.
   
    

  
  77.  Computational complexity:  On the geometry of polynomials and a theory of
cost, Part II (with Mike Shub),  SIAM Journal of Computing,  15
(1986), pp. 145--161.
   
    

  
  78.  On the existence of generally convergent algorithms (with Mike Shub),
 Journal of Complexity,  2 (1986), pp. 2--11.
   
    

  
  79.  Newton's method estimates from data at one pint, The Merging of
Disciplines:   New Directions in Pure, Applied, and Computational
Mathematics, edited by Richard E. Ewing, Kenneth I. Gross, and Clyde F.
Martin, Springer--Verlag, New York, (1986), pp. 185--196.
   
    




  
  80.  On the topology of algorithms, I.,  Journal of Complexity,  3
(1987), pp. 81--89.
   
    

  
  81.  Algorithms for solving equations, Proceedings of the International
Congress of Mathematicians, August 3--11, 1986, Berkeley, California, USA, 
American Mathematical Society Providence, (1987), pp. 172--195.
   
    

  
  82.  Global analysis in economic theory, The New Palgrave:   A Dictionary
of Economics,  2, edited by John Eatwell, Murray Milgrate, and Peter
Newman,  Macmillan Press, (1987), London, pp. 532--534.
   
    

  
  83.  The Newtonian contribution to our understanding of the computer, 
Queen's Quarterly,  95 (1988), pp. 90--95.
   
    

  
  84.  On a theory of computation and complexity over the real numbers:
NP-completeness, recursive functions and universal machines (with Lenore Blum
and Mike Shub),  Bulletin (New Series) of the American Mathematical
Society,  21(1) (1989), pp. 1--46.
   
    

  
  85.  Some remarks on the foundations of numerical analysis,  SIAM Review,
 32(2) (1990), pp. 221--270.
   
    

  
  86.  The story of the higher dimensional Poincaré conjecture,  The
Mathematical Intelligencer,  21(2) (1990), pp. 40--51.
   
    

    

    
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  87.  Dynamics retrospective:  great problems, attempts that failed, 
Physica D,  51 (1991), pp. 267--273.
   
    
  
  88.  Theory of computation,  Mathematical Research Today Tomorrow, ed.
Casacuberta, Castellet Spring, New York, (1992), pp. 60--69.
   
    

  
  89.  Complexity of Bezout's Theorem I:  Geometric aspects (with Mike Shub),
 Journal of the American Mathematical Society,  6 (1993), pp.
459--501.
   
    


  
  90.  Complexity of Bezout's Theorem II:  Volumes and probabilities (with Mike
Shub), Computational Algebraic Geometry (F. Eyssette and A. Galligo,
eds.)  Progress in Mathematics, Birkhauser,  109 (1993), pp. 267--285.
   
    

  
  91.  Complexity of Bezout's Theorem III:  Condition number and packing (with
Mike Shub),  Journal of Complexity,  9 (1993), pp. 4--14.
   
    

  
  92.  What is Chaos, in Nobel Conference XXVI,  Chaos the New Science, ed.
J. Holte Gustavus Adolphus College, University Press in American, (1993), pp.
89--104.
   
    




  
  93.  Complexity of Bezout's Theorem V:  Polynomial Time (with Mike Shub), 
Theoretical Computer Science,  133 (1994), pp. 141--164
    
    

  
  94.  Separation of Complexity Classes in Koiran's Weak Model (with Felipé 
Cucker and Mike Shub),  Theoretical Computer Science,  133 (1994),
pp. 3--14.
   
    

  
  95.  Complexity of Bezout's Theorem IV:  Probabability of success;
Extensions (with Mike Shub),  SIAM Jour. of Numerical Analysis 
(1996).
   
    

  
  96.   On the Intractibility of Hilbert's Nullstellensatz and an Algebraic
Version of "NP=P?" (with Mike Shub)  Duke Math Jour  to appear.
  
    


  
  97.   Complexity and Real Computation: A Manifesto (with L. Blum,
F. Cucker and M. Shub)  International Journal of Bifurcation and
Chaos Vol. 6 No.1 (1996).
   
    

  
  98.  Algebraic Settings for the Problem "P=NP"  (with L. Blum,
F. Cucker, M. Shub) Lectures in Applied Mathematics, ed J. Renegar,
M. Shub and S. Smale  to appear 
   
    

  
  99.   Chaos: Finding a Horseshoe on the Beaches of Rio  to appear 
   
    






 


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Steve Smale

Last update: April 1996