On the existence of two-dimensional invariant tori for scalar parabolic equations with time periodic coefficients

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1. [1] S. Angenent, The zero set of a solution of a parabolic equation, J. Reine Angew. Math.396 (1988), 79-96. Zbl0644.35050MR953678
2. [2] P. Brunovsky - P. Pola B. Sanstede, Convergence in general parabolic equations in one space dimension, preprint. 
3. [3] X. Chen - H. Matano, Convergence, asymptotic periodicity and finite time blow-up in one space dimension semilinear heat equations, J. Differential Equations78 (1989), 159-172. Zbl0692.35013
4. [4] P. Chossat - M. Golubitsky, Hopf bifurcation in the presence of symmetry, centre manifolds and Liapounov-Schmidt reduction, p. 344-352 in "Oscillation, bifurcation and chaos", Amer Math Soc., Providence, 1987. Zbl0631.58021MR909923
5. [5] E.N. Dancer, The effect of domain shape on the number of positive solutions of certain nonlinear equations II, J. Differential Equations, 87 (1990), 316-339. Zbl0729.35050MR1072904
6. [6] M. Golubitsky - I. Stewart - D. Schaeffer, Singularities and groups in bifurcation theory II, Springer, Berlin, 1988. Zbl0691.58003MR950168
7. [7] D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics840, Springer, Berlin, 1981. Zbl0456.35001MR610244
8. [8] P. Hess, On positive solutions of semilinear periodic parabolic problems, in Infinite-dimensional systems, Lecture Notes in Mathematics1076, Springer, Berlin, 1984. Zbl0556.35066MR843583
9. [9] M. Hirsch - C. Pugh - M. Shub, Invariant manifolds, Lecture Notes in Mathematics, Vol. 583, Springer, Berlin, 1977. Zbl0355.58009MR501173
10. [10] G. looss, Bifurcation of maps and application, North Holland, Amsterdam, 1979. 
11. [11] T. Kato, Perturbation theory for linear operators, Springer, Berlin, 1966. Zbl0148.12601
12. [12] O. Ladyzhenskaya - V. Solonnikov - N. Uralceva, Linear and quasilinear equations of parabolic type, Amer. Math. Soc., Providence, 1981. Zbl0174.15403
13. [13] I. Mardesic - J. Segal, Shape theory, North Holland, Amsterdam, 1982. Zbl0495.55001MR676973
14. [14] P. Pola, Complicated dynamics in scalar semilinear parabolic equations in higher space dimension, to appear. MR1091478
15. [15] D. Ruelle - F. Takens, On the nature of turbulence, Comm. Math. Phys.20 (1972), 167-192. Zbl0223.76041MR284067
16. [16] S. Stenberg, Celestial mechanics - Part II, Benjamin, New York, 1969. Zbl0194.56702
17. [17] A. Vanderbauwhede, Invariant manifolds in infinite dimensions, 409-420 in "Dynamics of infinite dimensional systems", Springer, Berlin, 1987. MR921925

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