Regularity of embeddings of infinite-dimensional fractal sets into finite-dimensional spaces

Nonlinearity

Volumn 12, Issue 5, 1999, Pages 1263-1275

  Hunt, Brian R ^a   Yu Kaloshin, Vadim ^b  

^a Bldg 142   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033196607     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/12/5/303     Document Type: Article

References (41)

1. Arnold V I, Gusein-Zade S M and Varchenko A N 1985 Singularities of Differentiable Maps vol 1 (Boston, MA: Birkhauser)
2. Babin A V and Vishik M I 1983 Regular attractors of semigroups and evolution equations J. Math. Pures Appl. 62 441-91
3. Ben-Artzi A, Eden A, Foias C and Nicolaenko B 1993 Hölder continuity for the inverse of Mañé's projection J. Math. Anal. Appl. 178 22-9
4. Constantin P and Foias C 1985 Global Lyapunov exponents, Kaplan-Yorke formulae and the dimension of the attractors for 2D Navier-Stokes equations Commun. Pure Appl. Math. 38 1-27
5. Constantin P, Foias C and Temam R 1985 Attractors representing turbulent flows Mem. Am. Math. Soc. 53 314
6. Constantin P, Foias C and Temam R 1988 On the dimension of the attractors in two-dimensional turbulence Physica D 30 284-96
7. Eckmann J-P and Ruelle D 1985 Ergodic theory of chaos and strange attractors Rev. Mod. Phys. 57 617-56
8. Eden A, Foias C, Nicolaenko B and Temam R 1994 Exponential Attractors for Dissipative Evolution Equations (Res. Appl. Math.) (New York: Wiley)
9. Falconer K 1990 Fractal Geometry: Mathematical Foundations and Applications (New York: Wiley)
10. Falconer K and Howroyd J D 1996 Projection theorems for box and packing dimensions Math. Proc. Camb. Phil. Soc. 119 287-95
11. Foias C and Olson E 1996 Finite fractal dimension and Hölder-Lipschitz parametrization Indiana Univ. Math. J. 45 603
12. Foias C and Temam R 1979 Some analytic and geometric properties of the solutions of the Navier-Stokes equations J. Math. Pures Appl. 58 339-68
13. Friz P and Robinson J Smooth attractors have zero 'thickness' Preprint
14. Frostman O 1935 Potential d'équilibre et capacité des ensembles avec quelques applications à la théorie des fonctions Meddel. Lunds Univ. Math. Sem. 3 1-118
15. Hale J K 1988 Asymptotic behaviour of dissipative systems (Math. Surveys and Monographs vol 25) (Providence, RI: American Mathematical Society)
16. Hunt B R and Yu Kaloshin V 1997 How projections affect the dimension spectrum of fractal measures Nonlinearity 10 1031-46
17. Hunt B R, Sauer T and Yorke J A 1992 Prevalence: a translation-invariant almost every for infinite dimensional spaces Bull. Am. Math. Soc. 27 217-38 Hunt B R, Sauer T and Yorke J A 1993 Prevalence: an addendum Bull. Am. Math. Soc. 28 306-7
18. Hunt B R, Sauer T and Yorke J A 1992 Prevalence: a translation-invariant almost every for infinite dimensional spaces Bull. Am. Math. Soc. 27 217-38 Hunt B R, Sauer T and Yorke J A 1993 Prevalence: an addendum Bull. Am. Math. Soc. 28 306-7
19. Järvenpää M 1994 On the upper Minkowski dimension, the packing dimension, and orthogonal projections Ann. Acad. Sci. Fenn. Math. Diss. 99 1-34
20. Yu Kaloshin V 1996 Some prevalent properties of smooth dynamical systems Differential Equations with Complex and Real Time, (Proc. Steklov Inst. Math. vol 213) ed Yu S Il'yashenko (Moscow: Maik Nauka)
21. Kaufmann R 1968 On Hausdorff dimension of projections Mathematika 15 153-5
22. Kupka I 1963 Contribution à la théorie des champs génériques Contrib. Diff. Eqn 2 457-84 Kupka I 1964 Contrib. Diff. Eqn 3 411-20
23. Kupka I 1963 Contribution à la théorie des champs génériques Contrib. Diff. Eqn 2 457-84 Kupka I 1964 Contrib. Diff. Eqn 3 411-20
24. Ladyzhenskaya O A 1985 On the finiteness of the dimension of bounded invariant sets for the Navier-Stokes equations and other related dissipative systems J. Sov. Math. 28 714-25
25. Mallet-Paret J 1976 Negatively invariant sets of compact maps and an extension of a theorem of Cartwright J. Diff. Eqns 22 331
26. 1 flows Geometry and Topology (Lecture Notes in Mathematics vol 597) (Berlin: Springer) pp 361-78
27. Mañé R 1981 On the dimension of the compact invariant sets of certain non-linear maps Dynamical Systems and Turbulence (Lecture Notes in Mathematics vol 898) (Berlin: Springer) pp 230-42
28. Marstrard J M 1954 Some fundamental geometrical properties of plane sets of fractional dimension Proc. London Math. Soc. 4 257-302
29. Mattila P 1975 Hausdorff dimension, orthogonal projections and intersections with planes Ann. Acad. Sci. Fenn. A 1 227-44
30. Mattila P 1995 Geometry of Sets and Measures in Euclidean Spaces (Cambridge: Cambridge University Press)
31. Nicolaenko B, Scheurer B and Temam R 1985 Some global dynamical properties of the Kuramoto-Sivashinsky equations Physica D 16 155-83
32. Nicolaenko B, Scheurer B and Temam R 1988 Some global dynamical properties of a class of pattern formation equations Commun. Part. Diff. Eqns 14 245-97
33. Palis J and de Melo W 1982 Geometric Theory of Dynamical Systems: An Introduction (New York: Springer) translated by A K Manning
34. Sauer T and Yorke J A 1997 Are the dimensions of a set and its image equal under typical smooth functions? Ergod. Theor. Dynam. Sys. 17 941-56
35. Sauer T, Yorke J A and Casdagli M 1993 Embedology J. Stat. Phys. 71 529-47
36. Smale S 1963 Stable manifolds for differential equations and diffeomorphisms Ann. Sci. Norm. Sup. Pisa 18 97-116
37. Takens F 1981 Detecting strange attractors in turbulence Dynamical Systems and Turbulence (Lecture Notes in Mathematics vol 898) (New York: Springer) pp 366-81
38. Temam R 1985 Attractors for Navier-Stokes equations Nonlinear Partial Differential Equations and Their Applications vol VII (Research Notes in Mathematics vol 122) (London: Pitman)
39. Temam R 1985 Attractors for Navier-Stokes equations Nonlinear Partial Differential Equations and Their Applications vol VII (Research Notes in Mathematics vol 122) (London: Pitman)
40. Temam R 1988 Infinite Dimensional Dynamical Systems in Mechanics and Physics (Appl. Math. Sci. vol 68) (New York: Springer)
41. Whitney H 1963 Differentiable manifolds Ann. Math. 37 645-80