Difference Equations and Dynamical Systems Generated by Certain Classes of Boundary Value Problems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems and related problems of geometry, Tome 244 (2004), pp. 281-296.

Voir la notice de l'article provenant de la source Math-Net.Ru

A special class of evolution semigroups is considered. The study of these semigroups can be reduced to the analysis of the dynamical properties of maps with one- or two-dimensional phase space. The structure of attractors and the entropy properties of appropriate infinite-dimensional dynamical systems are described.
@article{TM_2004_244_a10,
     author = {A. N. Sharkovskii and E. Yu. Romanenko},
     title = {Difference {Equations} and {Dynamical} {Systems} {Generated} by {Certain} {Classes} of {Boundary} {Value} {Problems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {281--296},
     publisher = {mathdoc},
     volume = {244},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2004_244_a10/}
}
TY  - JOUR
AU  - A. N. Sharkovskii
AU  - E. Yu. Romanenko
TI  - Difference Equations and Dynamical Systems Generated by Certain Classes of Boundary Value Problems
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2004
SP  - 281
EP  - 296
VL  - 244
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2004_244_a10/
LA  - ru
ID  - TM_2004_244_a10
ER  - 
%0 Journal Article
%A A. N. Sharkovskii
%A E. Yu. Romanenko
%T Difference Equations and Dynamical Systems Generated by Certain Classes of Boundary Value Problems
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2004
%P 281-296
%V 244
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2004_244_a10/
%G ru
%F TM_2004_244_a10
A. N. Sharkovskii; E. Yu. Romanenko. Difference Equations and Dynamical Systems Generated by Certain Classes of Boundary Value Problems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems and related problems of geometry, Tome 244 (2004), pp. 281-296. http://geodesic.mathdoc.fr/item/TM_2004_244_a10/

[1] Iwanik A., “Independent sets of transitive points”, Dynamical systems and ergodic theory, Banach Center Publ., 23, Pol. Sci. Publ., Warszawa, 1989, 277–282 | MR | Zbl

[2] Milnor J., “On the concept of attractor”, Commun. Math. Phys., 99 (1985), 177–195 | DOI | MR | Zbl

[3] Romanenko E. Yu., “On chaos in continuous difference equations”, Dynamical systems and applications, World Sci. Ser. Appl. Anal., 4, World Sci., Singapore, 1995, 617–630 | MR | Zbl

[4] Romanenko E. Yu., “On attractors of continuous difference equations”, Comput. Math. Appl., 36:10/12 (1999), 377–390 | DOI | MR

[5] Romanenko E. Yu., Sharkovskii A. N., “Ot odnomernykh k beskonechnomernym dinamicheskim sistemam: idealnaya turbulentnost”, (na ukr. yaz.), Ukr. mat. zhurn., 48:12 (1996), 1604–1627 | MR | Zbl

[6] Romanenko E. Yu., Sharkovskii A. N., “Dinamika reshenii prosteishikh nelineinykh kraevykh zadach”, Ukr. mat. zhurn., 51:6 (1999), 810–826 | MR | Zbl

[7] Romanenko E. Yu., Sharkovsky A. N., “From boundary value problems to difference equations: A method of investigation of chaotic vibrations”, Intern. J. Bifurcation and Chaos, 9:7 (1999), 1285–1306 | DOI | MR | Zbl

[8] Romanenko E. Yu., Sharkovsky A. N., Vereikina M. B., “Self-structuring and self-similarity in boundary value problems”, Intern. J. Bifurcation and Chaos, 5:5 (1995), 1407–1418 | DOI | MR | Zbl

[9] Romanenko E. Yu., Sharkovsky A. N., Vereikina M. B., “Structural turbulence in boundary value problems”, Control of oscillations and chaos, St. Petersburg, 1997, 492–497

[10] Romanenko E. Yu., Sharkovsky A. N., Vereikina M. B., “Self-structuring and self-stochasticity in difference equations and some boundary value problems”, Self-similar systems, Proc. workshop, JINR, Dubna, 1999., 237–250 | MR

[11] Sharkovsky A. N., “Ideal turbulence in an idealized time-delayed Chua's circuit”, Intern. J. Bifurcation and Chaos, 4:2 (1994), 303–309 | DOI | MR | Zbl

[12] Sharkovsky A. N., “Universal phenomena in some infinite-dimensional dynamical systems”, Intern. J. Bifurcation and Chaos, 5:5 (1995), 1419–1425 | DOI | MR | Zbl

[13] Sharkovskii A. N., Kolyada S. F., Sivak A. G., Fedorenko V. V., Dinamika odnomernykh otobrazhenii, Nauk. dumka, Kiev, 1989, 216 pp. ; Sharkovsky A. N., Kolyada S. F., Sivak A. G., Fedorenko V. V., Dynamics of one-dimensional mappings, Math. and Appl., 407, Kluwer Acad. Publ., Dordrecht, 1997, 262 pp. | MR | MR | Zbl

[14] Sharkovskii A. N., Maistrenko Yu. L., Romanenko E. Yu., Raznostnye uravneniya i ikh prilozheniya, Nauk. dumka, Kiev, 1986, 280 pp. ; Sharkovsky A. N., Maistrenko Yu. L., Romanenko E. Yu., Difference equations and their applications, Math. and Appl., 250, Kluwer Acad. Publ., Dordrecht, 1993, 358 pp. | MR | MR

[15] Sharkovskii A. N., Maistrenko Yu. L., Romanenko E. Yu., “Asimptoticheskaya periodichnost reshenii raznostnykh uravnenii s nepreryvnym vremenem”, Ukr. mat. zhurn., 39:1 (1987), 123–129 | MR

[16] Sharkovsky A. N., Romanenko E. Yu., “Ideal turbulence: Attractors of deterministic systems may lie in the space of random fields”, Intern. J. Bifurcation and Chaos, 2:1 (1992), 31–36 | DOI | MR | Zbl

[17] Sharkovskii A. N., Romanenko E. Yu., “Avtostokhastichnost: attraktory determinirovannykh zadach mogut soderzhat sluchainye funktsii”, (na ukr. yaz.), Dop. NAN Ukr., 1992, no. 10, 33–37 | MR

[18] Sharkovsky A. N., Sivak A. G., “Universal phenomena in solution bifurcations of some boundary value problems”, J. Nonlin. Math. Phys., 1:2 (1994), 147–157 | DOI | MR | Zbl

[19] Fedorenko V. V., “Topologicheskii predel traektorii intervala prosteishikh odnomernykh dinamicheskikh sistem”, Ukr. mat. zhurn., 54:3 (2002), 425–430 | MR | Zbl