Realizing vector fields without loss of derivatives

Martino Prizzi

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1998)

  • Volume: 27, Issue: 2, page 289-307
  • ISSN: 0391-173X

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Prizzi, Martino. "Realizing vector fields without loss of derivatives." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 27.2 (1998): 289-307. <http://eudml.org/doc/84359>.

@article{Prizzi1998,
author = {Prizzi, Martino},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {center manifold; delay differential equations},
language = {eng},
number = {2},
pages = {289-307},
publisher = {Scuola normale superiore},
title = {Realizing vector fields without loss of derivatives},
url = {http://eudml.org/doc/84359},
volume = {27},
year = {1998},
}

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
PB - Scuola normale superiore
VL - 27
IS - 2
SP - 289
EP - 307
LA - eng
KW - center manifold; delay differential equations
UR - http://eudml.org/doc/84359
ER -

References

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  1. [1] S.N. Chow - K. Lu, Invariant manifolds for flows in Banach spaces, J. Differential Equations74 (1988), 285-317. Zbl0691.58034MR952900
  2. [2] E.N. Dancer - P. Polá, Realization of vector fields and dynamics of spatially homogeneous parabolic equations, preprint. MR1618487
  3. [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. A125 (1995), 759-776. Zbl0835.34086MR1357382
  4. [4] T. Faria - L. Magalhães, Normal forms for retardedfunctional differential equations and applications to bogdanov-takens singularity, J. Differential Equations122 (1995), 201-224. Zbl0836.34069MR1355889
  5. [5] T. Faria - L. Magalhães, Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation, J. Differential Equations122 (1995), 181-200. Zbl0836.34068MR1355888
  6. [6] T. Faria - L. Magalhães, Restrictions on the possible flows of scalar retarded functional differential equations in neighborhoods of singularities, J. Dynam. Differential Equations8 (1996) 35-70. Zbl0853.34064MR1388164
  7. [7] B. Fiedler - P. Polá, Complicated dynamics of scalar reaction-diffusion equations with a nonlocal term, Proc. Roy. Soc. Edinburgh Sect. A115 (1990), 167-192. Zbl0726.35060MR1059652
  8. [8] B. Fiedler - B. Sandstede, Dynamics of periodically forced parabolic equations on the circle, Ergodic Theory Dynam. Systems12 (1992), 559-571. Zbl0754.35066MR1182662
  9. [9] J.K. Hale - S.M. Verduyn Lunel, "Introduction to Functional Differential Equations ", Springer-Verlag, BerlinHeidelberg, New York, 1993. Zbl0787.34002MR1243878
  10. [10] J.K. Hale, Flows on centre manifolds for scalar functional differential equations, Proc. Roy. Soc. Edinburgh Sect.A101 (1985), 193-201. Zbl0582.34058MR824220
  11. [11] D. Henri, "Geometric Theory of Semilinear Parabolic Equations", Lecture Notes in Mathematics, Vol 840, Springer-Verlag, NY, 1981. Zbl0456.35001MR610244
  12. [12] H. Matano, Convergence of solutions of one-dimensional semilinear parabolic equations, J. Math. Kyoto Univ.18 (1978), 221-227. Zbl0387.35008MR501842
  13. [13] P Poláčik, Complicated dynamics in scalar semilinear parabolic equations in higher space dimension, J. Differential Equations89 (1991), 244-271. Zbl0738.35027MR1091478
  14. [14] P Poláčik, Imbedding of any vector field in a scalar semilinear parabolic equation, Proc. Amer. Math. Soc.115 (1992), 1001-1008. Zbl0755.35046MR1089411
  15. [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. Zbl0774.35041MR1118222
  16. [16] P Poláčik, High-dimensional ω-limit sets and chaos in scalar parabolic equations, J. Differential Equations119 (1995), 24-53. Zbl0830.35060
  17. [17] P Poláčik, Reaction-diffusion equations and realization of gradient vector fields, Proc. Equadiff. (1995), (to appear). MR1639355
  18. [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. Zbl0852.35074MR1375317
  19. [19] P Poláčik - K.P. Rybakowski, Nonconvergent bounded trajectories in semilinear heat equations, J. Differential Equations124 (1995), 472-494. Zbl0845.35054MR1370152
  20. [20] M. Prizzi - K.P. Rybakowski, Complicated dynamics of parabolic equations with simple gradient dependence, Trans. Amer. Math. Soc.350 (1998), 3119-3130. Zbl0897.35040MR1491875
  21. [21] M. Prizzi - K.P. Rybakowski, Inverse problems and chaotic dynamics of parabolic equations on arbitrary spatial domains, J. Differential Equations142 (1998), 17-53. Zbl0915.35059MR1492876
  22. [22] M. Prizzi, Perturbation of elliptic operators and complex dynamics of parabolic PDEs, preprint. 
  23. [23] K.P. Rybakowski, An abstract approach to smoothness of invariant manifolds, Appl. Anal.49 (1993), 119-150. Zbl0736.35016MR1279237
  24. [24] K.P. Rybakowski, Realization of arbitrary vector fields on center manifolds ofparabolic dirichlet BVPs, J. Differential Equations114 (1994), 199-221. Zbl0807.35072MR1302140
  25. [25] K.P. Rybakowski, Realization of arbitrary vector fields on invariant manifolds of delay equations, J. Differential Equations114 (1994), 222-231. Zbl0815.34064MR1302141
  26. [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. Frigon472, Kluwer Academic Publishers, Dordrecht/Boston /London, 1995, pp. 411-446. Zbl0840.35048MR1368677

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