Realizing vector fields without loss of derivatives
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 27 (1998) no. 2, pp. 289-307.
@article{ASNSP_1998_4_27_2_289_0,
     author = {Prizzi, Martino},
     title = {Realizing vector fields without loss of derivatives},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {289--307},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 27},
     number = {2},
     year = {1998},
     mrnumber = {1664690},
     zbl = {0937.35090},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_1998_4_27_2_289_0/}
}
TY  - JOUR
AU  - Prizzi, Martino
TI  - Realizing vector fields without loss of derivatives
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1998
SP  - 289
EP  - 307
VL  - 27
IS  - 2
PB  - Scuola normale superiore
UR  - http://archive.numdam.org/item/ASNSP_1998_4_27_2_289_0/
LA  - en
ID  - ASNSP_1998_4_27_2_289_0
ER  - 
%0 Journal Article
%A Prizzi, Martino
%T Realizing vector fields without loss of derivatives
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1998
%P 289-307
%V 27
%N 2
%I Scuola normale superiore
%U http://archive.numdam.org/item/ASNSP_1998_4_27_2_289_0/
%G en
%F ASNSP_1998_4_27_2_289_0
Prizzi, Martino. Realizing vector fields without loss of derivatives. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 27 (1998) no. 2, pp. 289-307. http://archive.numdam.org/item/ASNSP_1998_4_27_2_289_0/

[1] S.N. Chow - K. Lu, Invariant manifolds for flows in Banach spaces, J. Differential Equations 74 (1988), 285-317. | MR | Zbl

[2] E.N. Dancer - P. Polá, Realization of vector fields and dynamics of spatially homogeneous parabolic equations, preprint. | MR

[3] T. Faria - L. Magalhães, Realization of ordinary differential equations by retarded functional differential equations in neighborhoods of equilibrium points, Proc. Roy. Soc. Edinburgh Sect. A 125 (1995), 759-776. | MR | Zbl

[4] T. Faria - L. Magalhães, Normal forms for retardedfunctional differential equations and applications to bogdanov-takens singularity, J. Differential Equations 122 (1995), 201-224. | MR | Zbl

[5] T. Faria - L. Magalhães, Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation, J. Differential Equations 122 (1995), 181-200. | MR | Zbl

[6] T. Faria - L. Magalhães, Restrictions on the possible flows of scalar retarded functional differential equations in neighborhoods of singularities, J. Dynam. Differential Equations 8 (1996) 35-70. | MR | Zbl

[7] B. Fiedler - P. Polá, Complicated dynamics of scalar reaction-diffusion equations with a nonlocal term, Proc. Roy. Soc. Edinburgh Sect. A 115 (1990), 167-192. | MR | Zbl

[8] B. Fiedler - B. Sandstede, Dynamics of periodically forced parabolic equations on the circle, Ergodic Theory Dynam. Systems 12 (1992), 559-571. | MR | Zbl

[9] J.K. Hale - S.M. Verduyn Lunel, "Introduction to Functional Differential Equations ", Springer-Verlag, Berlin Heidelberg, New York, 1993. | MR | Zbl

[10] J.K. Hale, Flows on centre manifolds for scalar functional differential equations, Proc. Roy. Soc. Edinburgh Sect. A 101 (1985), 193-201. | MR | Zbl

[11] D. Henri, "Geometric Theory of Semilinear Parabolic Equations", Lecture Notes in Mathematics, Vol 840, Springer-Verlag, NY, 1981. | MR | Zbl

[12] H. Matano, Convergence of solutions of one-dimensional semilinear parabolic equations, J. Math. Kyoto Univ. 18 (1978), 221-227. | MR | Zbl

[13] P Poláčik, Complicated dynamics in scalar semilinear parabolic equations in higher space dimension, J. Differential Equations 89 (1991), 244-271. | MR | Zbl

[14] P Poláčik, Imbedding of any vector field in a scalar semilinear parabolic equation, Proc. Amer. Math. Soc. 115 (1992), 1001-1008. | MR | Zbl

[15] P Poláčik, Realization of any finite jet in a scalar semilinear equation on the ball in R3, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 18 (1991), 83-102. | Numdam | MR | Zbl

[16] P Poláčik, High-dimensional ω-limit sets and chaos in scalar parabolic equations, J. Differential Equations 119 (1995), 24-53. | Zbl

[17] P Poláčik, Reaction-diffusion equations and realization of gradient vector fields, Proc. Equadiff. (1995), (to appear). | MR

[18] P Poláčik - K.P. Rybakowski, Imbedding vector fields in scalar parabolic dirichlet BVPs, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 22 (1995), 737-749. | Numdam | MR | Zbl

[19] P Poláčik - K.P. Rybakowski, Nonconvergent bounded trajectories in semilinear heat equations, J. Differential Equations 124 (1995), 472-494. | MR | Zbl

[20] M. Prizzi - K.P. Rybakowski, Complicated dynamics of parabolic equations with simple gradient dependence, Trans. Amer. Math. Soc. 350 (1998), 3119-3130. | MR | Zbl

[21] M. Prizzi - K.P. Rybakowski, Inverse problems and chaotic dynamics of parabolic equations on arbitrary spatial domains, J. Differential Equations 142 (1998), 17-53. | MR | Zbl

[22] M. Prizzi, Perturbation of elliptic operators and complex dynamics of parabolic PDEs, preprint.

[23] K.P. Rybakowski, An abstract approach to smoothness of invariant manifolds, Appl. Anal. 49 (1993), 119-150. | MR | Zbl

[24] K.P. Rybakowski, Realization of arbitrary vector fields on center manifolds ofparabolic dirichlet BVPs, J. Differential Equations 114 (1994), 199-221. | MR | Zbl

[25] K.P. Rybakowski, Realization of arbitrary vector fields on invariant manifolds of delay equations, J. Differential Equations 114 (1994), 222-231. | MR | Zbl

[26] K.P. Rybakowski, The center manifold technique and complex dynamics of parabolic equations, In "Topological Methods in Differential Equations and Inclusions" NATO ASI Series A. Granas M. Frigon 472, Kluwer Academic Publishers, Dordrecht/Boston /London, 1995, pp. 411-446. | MR | Zbl