Optimal Cycles and Chaos

  • Tapan Mitra
  • Kazuo Nishimura
  • Gerhard Sorger
Chapter

Keywords

Utility Function Discount Factor Periodic Point Optimal Program Optimal Cycle 
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Bibliography

  1. [1]
    R. Amir (1996), “Sensitivity analysis of multisector optimal economic dynamics”, Journal of Mathematical Economics 25, 123–141.MATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    J. Benhabib and R. Day (1982), “Rational choice and erratic behaviour”, Review of Economic Studies 48, 459–471.MathSciNetGoogle Scholar
  3. [3]
    J. Benhabib and K. Nishimura (1985), “Competitive equilibrium cycles”, Journal of Economic Theory 35, 284–306.MathSciNetCrossRefGoogle Scholar
  4. [4]
    M. Boldrin and R.J. Deneckere (1990), “Sources of complex dynamics in two-sector growth models”, Journal of Economic Dynamics and Control 14, 627–653.MathSciNetCrossRefGoogle Scholar
  5. [5]
    M. Boldrin and L. Montrucchio (1986), “On the indeterminacy of capital accumulation paths”, Journal of Economic Theory 40, 26–39.MathSciNetCrossRefGoogle Scholar
  6. [6]
    W.A. Brock (1970), “On existence of weakly maximal programmes in a multi-sector economy”, Review of Economic Studies 37, 275–280.MATHCrossRefGoogle Scholar
  7. [7]
    G. Butler and G. Pianigiani (1978), “Periodic points and chaotic functions in the unit interval”, Bulletin of the Australian Mathematical Society 18, 255–265.MathSciNetCrossRefGoogle Scholar
  8. [8]
    D. Cass and K. Shell (1976), “The structure and stability of competitive dynamical systems”, Journal of Economic Theory 12, 31–70.MathSciNetCrossRefGoogle Scholar
  9. [9]
    R.H. Day (1982), “Irregular growth cycles”, American Economic Review 72, 406–414.Google Scholar
  10. [10]
    R.H. Day (1983), “The emergence of chaos from classical economic growth”, Quarterly Journal of Economics 98, 201–213.MathSciNetCrossRefGoogle Scholar
  11. [11]
    R. Deneckere and S. Pelikan (1986), “Competitive chaos”, Journal of Economic Theory 40, 13–25.MathSciNetCrossRefGoogle Scholar
  12. [12]
    D. Gale (1967), “On optimal development in a multi-sector economy”, Review of Economic Studies 34, 1–18.MathSciNetCrossRefGoogle Scholar
  13. [13]
    M.A. Khan and T. Mitra (2005), “On topological chaos in the Robinson-Solow-Srinivasan model”, Economics Letters 88, 127–133.MathSciNetCrossRefGoogle Scholar
  14. [14]
    M. Kurz (1968), “Optimal growth and wealth effects”, International Economic Review 9, 348–357.MATHCrossRefGoogle Scholar
  15. [15]
    A. Lasota and J.A. Yorke (1973), “On the existence of invariant measures for piecewise monotonic transformations”, Transactions of the American Mathematical Society 186, 481–488.MathSciNetCrossRefGoogle Scholar
  16. [16]
    T. Li and J. Yorke (1975), “Period three implies chaos”, American Mathematical Monthly 82, 985–992.MathSciNetCrossRefGoogle Scholar
  17. [17]
    T. Li and J. Yorke (1978), “Ergodic transformations from an interval into itself”, Transactions of the American Mathematical Society 235, 183–192.MathSciNetCrossRefGoogle Scholar
  18. [18]
    L.W. McKenzie (1968), “Accumulation programs of maximum utility and the von Neumann facet”, in J.N. Wolfe, Value, Capital and Growth, Edinburgh University Press, 353–383.Google Scholar
  19. [19]
    L.W. McKenzie (1983), “Turnpike theory, discounted utility and the von Neumann facet”, Journal of Economic Theory 30, 330–352.MATHMathSciNetCrossRefGoogle Scholar
  20. [20]
    L.W. McKenzie (1986), “Optimal economic growth, turnpike theorems and comparative dynamics”, in K. Arrow and M. Intriligator, Handbook of Mathematical Economics III, North-Holland, 1281–1355.Google Scholar
  21. [21]
    T. Mitra (2000), “Introduction to dynamic optimization theory”, in M. Majumdar, T. Mitra, and K. Nishimura, Optimization and Chaos, Springer-Verlag, 31–108.Google Scholar
  22. [22]
    T. Mitra and K. Nishimura (2001), “Discounting and long-run behavior: global bifurcation analysis of a family of dynamical systems”, Journal of Economic Theory 96, 256–293.MathSciNetCrossRefGoogle Scholar
  23. [23]
    K. Nishimura and M. Yano (1994), “Optimal chaos, nonlinearity and feasibility conditions”, Economic Theory 4, 689–704.MathSciNetCrossRefGoogle Scholar
  24. [24]
    K. Nishimura and M. Yano (1995a), “Durable capital and chaos in competitive business cycles”, Journal of Economic Behavior and Organization 27, 165–181.CrossRefGoogle Scholar
  25. [25]
    K. Nishimura and M. Yano (1995b), “Nonlinear dynamics and chaos in optimal growth: an example”, Econometrica 63, 981–1001.MathSciNetCrossRefGoogle Scholar
  26. [26]
    K. Nishimura and M. Yano (1996), “Chaotic solutions in dynamic linear programming”, Chaos, Solitons & Fractals 7, 1941–1953.MathSciNetCrossRefGoogle Scholar
  27. [27]
    K. Nishimura, T. Shigoka, and M. Yano (1998), “Interior optimal chaos with arbitrarily low discount rates”, Japanese Economic Review 49, 223–233.CrossRefGoogle Scholar
  28. [28]
    K. Nishimura, G. Sorger, and M. Yano (1994), “Ergodic chaos in optimal growth models with low discount rates”, Economic Theory 4, 705–717.MathSciNetCrossRefGoogle Scholar
  29. [29]
    F.P. Ramsey (1928), “A mathematical theory of saving”, Economic Journal 38, 543–559.CrossRefGoogle Scholar
  30. [30]
    S.M. Ross (1983), Introduction to Stochastic Dynamic Programming, Academic Press.Google Scholar
  31. [31]
    P.A. Samuelson (1973), “Optimality of profit, including prices under ideal planning”, Proceedings of the National Academy of Sciences 70, 2109–2111.MATHMathSciNetCrossRefADSGoogle Scholar
  32. [32]
    A. Sarkovskii (1964), “Coexistence of cycles of a continuous map of the line into itself”, Ukrainian Mathematical Journal 16, 61–71.MathSciNetGoogle Scholar
  33. [33]
    J.A. Scheinkman (1976), “On optimal steady states of n-sector growth models when utility is discounted”, Journal of Economic Theory 12, 11–30.MATHMathSciNetCrossRefGoogle Scholar
  34. [34]
    G. Sorger (1992), Minimum Impatience Theorems for Recursive Economic Models, Springer-Verlag.Google Scholar
  35. [35]
    N.L. Stokey and R.E. Lucas, Jr., (1989), Recursive Methods in Economic Dynamics, Harvard University Press.Google Scholar
  36. [36]
    W.R.S. Sutherland (1970), “On optimal development in a multi-sectoral economy: the discounted case”, Review of Economic Studies 37, 585–589.MATHCrossRefGoogle Scholar
  37. [37]
    D. Topkis (1978), “Minimizing a submodular function on a lattice”, Operations Research 26, 305–321.MATHMathSciNetCrossRefGoogle Scholar
  38. [38]
    H. Uzawa (1964), “Optimal growth in a two-sector model of capital accumulation”, Review of Economic Studies 31, 1–24.CrossRefGoogle Scholar

Copyright information

© Springer Berlin · Heidelberg 2006

Authors and Affiliations

  • Tapan Mitra
    • 1
  • Kazuo Nishimura
    • 2
  • Gerhard Sorger
    • 3
  1. 1.Department of EconomicsCornell UniversityIthacaUSA
  2. 2.Institute of Economic ResearchKyoto UniversityJapan
  3. 3.Department of EconomicsUniversity of ViennaAustria

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