no. 3
On the existence of two-dimensional invariant tori for scalar parabolic equations with time periodic coefficients
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 18 (1991) no. 3, pp. 455-471. 
@article{ASNSP_1991_4_18_3_455_0,
     author = {Dancer, Edward Norman},
     title = {On the existence of two-dimensional invariant tori for scalar parabolic equations with time periodic coefficients},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {455--471},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 18},
     number = {3},
     year = {1991},
     zbl = {0779.35049},
     mrnumber = {1145318},
     language = {en},
     url = {www.numdam.org/item/ASNSP_1991_4_18_3_455_0/}
}
Dancer, E. N. On the existence of two-dimensional invariant tori for scalar parabolic equations with time periodic coefficients. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 18 (1991) no. 3, pp. 455-471. http://www.numdam.org/item/ASNSP_1991_4_18_3_455_0/

[1] S. Angenent, The zero set of a solution of a parabolic equation, J. Reine Angew. Math. 396 (1988), 79-96. | MR 953678 | Zbl 0644.35050

[2] P. Brunovsky - P. Pola B. Sanstede, Convergence in general parabolic equations in one space dimension, preprint.

[3] X. Chen - H. Matano, Convergence, asymptotic periodicity and finite time blow-up in one space dimension semilinear heat equations, J. Differential Equations 78 (1989), 159-172. | Zbl 0692.35013

[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. | MR 909923 | Zbl 0631.58021

[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. | MR 1072904 | Zbl 0729.35050

[6] M. Golubitsky - I. Stewart - D. Schaeffer, Singularities and groups in bifurcation theory II, Springer, Berlin, 1988. | MR 950168 | Zbl 0691.58003

[7] D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics 840, Springer, Berlin, 1981. | MR 610244 | Zbl 0456.35001

[8] P. Hess, On positive solutions of semilinear periodic parabolic problems, in Infinite-dimensional systems, Lecture Notes in Mathematics 1076, Springer, Berlin, 1984. | MR 843583 | Zbl 0556.35066

[9] M. Hirsch - C. Pugh - M. Shub, Invariant manifolds, Lecture Notes in Mathematics, Vol. 583, Springer, Berlin, 1977. | MR 501173 | Zbl 0355.58009

[10] G. Looss, Bifurcation of maps and application, North Holland, Amsterdam, 1979.

[11] T. Kato, Perturbation theory for linear operators, Springer, Berlin, 1966. | Zbl 0148.12601

[12] O. Ladyzhenskaya - V. Solonnikov - N. Uralceva, Linear and quasilinear equations of parabolic type, Amer. Math. Soc., Providence, 1981. | Zbl 0174.15403

[13] I. Mardesic - J. Segal, Shape theory, North Holland, Amsterdam, 1982. | MR 676973 | Zbl 0495.55001

[14] P. Pola, Complicated dynamics in scalar semilinear parabolic equations in higher space dimension, to appear. | MR 1091478

[15] D. Ruelle - F. Takens, On the nature of turbulence, Comm. Math. Phys. 20 (1972), 167-192. | MR 284067 | Zbl 0223.76041

[16] S. Stenberg, Celestial mechanics - Part II, Benjamin, New York, 1969. | Zbl 0194.56702

[17] A. Vanderbauwhede, Invariant manifolds in infinite dimensions, 409-420 in "Dynamics of infinite dimensional systems", Springer, Berlin, 1987. | MR 921925