Extended spectral decompositions of the Renyi map

Chaos, solitons and fractals

Volumn 11, Issue 1, 2000, Pages 393-421

  Antoniou, I ^a,b,d   Melnikov, Yu ^a,b,c   Shkarin, S ^a,d   Suchanecki, Z ^a,b,e  

^a INTERNATIONAL SOLVAY INSTITUTES   (Belgium)

^b VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

^c ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

^d MOSCOW STATE UNIVERSITY   (Russian Federation)

^e WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICS; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL OPERATORS;

HILBERT SPACES; RENYI MAPS;

CHAOS THEORY;

EID: 0033940298     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(98)00309-9     Document Type: Article

References (34)

1. T. Petrosky, I. Prigogine, Thermodynamic limit, Hilbert space and the breaking of time symmetry, Chaos, Solitons and Fractals 11 (1-3) (2000) 373-382.
2. Antoniou I, Tasaki S. Generalized spectral decomposition of mixing dynamical systems. Int. J. Quantum Chemistry 1993;46:425-74.
3. Antoniou I, Dmitrieva L. Yu. Kuperin, Yu. Melnikov, Resonances and the extension of dynamics to rigged hilbert space. Int. J. Comput. Math. Appl. 1997;34:399-425.
4. Bandtlow OF, Antoniou I, Suchanecki Z. Resonances of dynamical systems and Fredholm-Riesz operators on rigged Hilbert spaces. Computers Math. Appl. 1997;34:95-102.
5. Suchanecki Z, Antoniou I, Tasaki S, Bandtlow OF. Rigged Hilbert spaces for chaotic dynamical systems. J. Math. Phys. 1996;37:5837-47.
6. I. Antoniou, S. Shkarin, Extended spectral decomposition of evolution operators, in: I. Antoniou, G. Lumer (Eds.), Generalized Functions, Operator Theory and Dynamical systems, Pitman Research Notes in Mathematics Series, Longman, New York 1998.
7. Rényi A. Representations for real numbers and their ergodic properties. Acta Math. Acad. Sci. Hungary 1957;8:477-93.
8. Lasota A, Mackey MC. Probabilistic Properties of Deterministic Systems 1985, Cambridge: Cambridge Univ. Press.
9. Roepstorff G. On the Exponential Decay of Correlations in Exact Dynamical Systems, preprint 1987, Princeton: Institute for Advanced Study.
10. Gaspard P. r-adic one dimensional maps and the Euler summation formula. J. Phys. A 1992;25:L483-485.
11. Hasegawa HH, Saphir WC. Decaying eigenstates for simple chaotic systems. Phys. Lett. A161 1992:471-6.
12. Antoniou I, Tasaki S. Spectral decomposition of the Renyi map. J. Phys. A 1993;26:73-94.
13. Robertson A, Robertson V. Topological vector spaces 2nd edition 1973, Cambridge: Cambridge University Press.
14. Riesz F, Sz.-Nagy B. Leçons d'Analyse Fonctionnelle 1972, Budapest: Académiai Kiadó.
15. Brändas E, Elander N. Springer Resonances Lecture Notes in Physics 325 1989, Berlin: Springer.
16. Faddeev LD. Expansion in eigenfunctions of the Laplace operator on the fundamental domain of a discrete group on the Lobachevskij plane. Proc. Moscow Math. Soc. 1967;17:323-50.
17. Gelfand I, Vilenkin N. Generalized Functions Vol.4: Applications of Harmonic Analysis 1964, New York: Academic Press.
18. A. Böhm, M. Gadella, Dirac Kets, Gamow Vectors and Gelfand Triplets, Springer Lect are Notes in Physics 348, Springer, Berlin 1989.
19. I. Gradshtein, I. Ryzhik, Tables of Integrals, Sums, Series and Products Fizmatgiz, Moscow 1963.
20. Yu. Melnikov, Representation of the derivatives and products of the delta function in Hilbert space, in: I. Antoniou, G. Lumer, (Eds.), Generalized Functions, Operator Theory and Dynamical systems, Pitman Research Notes in Mathematics Series, Longman, New York, 1998, pp. 108-129.
21. Edwards RE. Functional analysis theory and applications 1965, New York: Holt Rinehart & Winston.
22. Kolmogorov AN, Fomin SV. Elements of the theory of functions and functional analysis 1961, Baltimore MD: Graylock Press.
23. I. Antoniou, V. Sadovnichii, S. Shkarin, New extended spectral decompositions of the Renyi map, Physics Letters A, in press (1999).
24. J.-P. Eckmann, Resonances in dynamical systems, in: B. Simon, et al. (Ed.), Proc. IX Int. Congr. on Mathematical Physics, Adam Hilger, Bristol 1989.
25. Grothendieck A. Topological Vector Spaces 1973, London: Gordon and Breach Science Publishers.
26. Heuser HG. Functional Analysis 1982, New York: Wiley Interscience.
27. Schaefer HH. Topological Vector Spaces 1971, New York: Springer.
28. Floret K, Wloka J. Einführung in die Theorie der Lokalkonvexen Räume, Springer Lecture Notes in Mathematics 56 1968, Berlin: Springer.
29. Treves F. Topological Vector Spaces, Distributions and Kernels 1967, New York: Academic Press.
30. I. Imai, Applied Hyperfunction Theory, Kluwer Academic Publishers, Dordrecht 1992.
31. Hata M. On the functional equation 1/p · {f(x/p) + ⋯ + f((x + p - 1}/p)} = λf(μx). J. Math. Kyoto Univ. 1985;25:357-64.
32. Bandtlow OF, Coveney PV. On the discrete time version of the Brussels formalism. J. Phys. A 1994;24:7939-55.
33. Edmunds DE, Evans WD. Spectral Theory of Differential Operators 1987, Oxford: Clarendon Press.
34. Boas RP, Buck RC. Polynomial expansions of analytic functions 1964, Berlin: Springer.