@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] The zero set of a solution of a parabolic equation, J. Reine Angew. Math. 396 (1988), 79-96. | MR 953678 | Zbl 0644.35050
,[2] Convergence in general parabolic equations in one space dimension, preprint.
- ,[3] 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] 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] 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] Singularities and groups in bifurcation theory II, Springer, Berlin, 1988. | MR 950168 | Zbl 0691.58003
- - ,[7] Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics 840, Springer, Berlin, 1981. | MR 610244 | Zbl 0456.35001
,[8] 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] Invariant manifolds, Lecture Notes in Mathematics, Vol. 583, Springer, Berlin, 1977. | MR 501173 | Zbl 0355.58009
- - ,[10] Bifurcation of maps and application, North Holland, Amsterdam, 1979.
,[11] Perturbation theory for linear operators, Springer, Berlin, 1966. | Zbl 0148.12601
,[12] Linear and quasilinear equations of parabolic type, Amer. Math. Soc., Providence, 1981. | Zbl 0174.15403
- - ,[13] Shape theory, North Holland, Amsterdam, 1982. | MR 676973 | Zbl 0495.55001
- ,[14] Complicated dynamics in scalar semilinear parabolic equations in higher space dimension, to appear. | MR 1091478
,[15] On the nature of turbulence, Comm. Math. Phys. 20 (1972), 167-192. | MR 284067 | Zbl 0223.76041
- ,[16] Celestial mechanics - Part II, Benjamin, New York, 1969. | Zbl 0194.56702
,[17] Invariant manifolds in infinite dimensions, 409-420 in "Dynamics of infinite dimensional systems", Springer, Berlin, 1987. | MR 921925
,