A one-parameter family of quadratic maps of a~plane including Morse--Smale endomorphisms
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2013), pp. 80-85.

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

In an one-parameter family of quadratic maps of a plane, we indicate an interval of parameter values such that every map with a parameter value in the indicated interval is a singular Morse–Smale endomorphism.
Keywords: quadratic map
Mots-clés : Morse–Smale endomorphism.
@article{IVM_2013_8_a7,
     author = {S. S. Bel'mesova and L. S. Efremova},
     title = {A one-parameter family of quadratic maps of a~plane including {Morse--Smale} endomorphisms},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {80--85},
     publisher = {mathdoc},
     number = {8},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_8_a7/}
}
TY  - JOUR
AU  - S. S. Bel'mesova
AU  - L. S. Efremova
TI  - A one-parameter family of quadratic maps of a~plane including Morse--Smale endomorphisms
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2013
SP  - 80
EP  - 85
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2013_8_a7/
LA  - ru
ID  - IVM_2013_8_a7
ER  - 
%0 Journal Article
%A S. S. Bel'mesova
%A L. S. Efremova
%T A one-parameter family of quadratic maps of a~plane including Morse--Smale endomorphisms
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2013
%P 80-85
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2013_8_a7/
%G ru
%F IVM_2013_8_a7
S. S. Bel'mesova; L. S. Efremova. A one-parameter family of quadratic maps of a~plane including Morse--Smale endomorphisms. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2013), pp. 80-85. http://geodesic.mathdoc.fr/item/IVM_2013_8_a7/

[1] Damanik D., Gorodetski A., “Hyperbolicity of the trace map for the weakly coupled Fibonacci hamiltonian”, Nonlinearity, 22 (2009), 123–143 | DOI | MR | Zbl

[2] Damanik D., Gorodetski A., “The spectrum of the weakly coupled Fibbonacci hamiltonian”, Elect. Research Announcements, Math. Sci., 16 (2009), 23–29 | DOI | MR | Zbl

[3] Avishai Y., Berend D., “Transmission through a one-dimensional Fibonacci sequence of $\delta$-function potentials”, Physical Review B, 41:9 (1990), 5492–5499 | DOI | MR

[4] Avishai Y., Berend D., Tkachenko V., “Trace maps”, Int. J. Modern Physics B, 11:30 (1997), 3525–3542 | DOI | MR | Zbl

[5] Sharkovskii A. N., “Problem list”, Int. Conf. “Low Dimensional Dynamics” (Oberwolfach, Germany, April 25 – May 1 1993), Tagungsbericht, 1993, 17

[6] Belmesova S. S., Efremova L. S., “O kvadratichnykh otobrazheniyakh nekotorogo odnoparametricheskogo semeistva, blizkikh k nevozmuschennomu”, Tr. MFTI, 2010, no. 2(2), 46–57

[7] Belmesova S. S., Efremova L. S., “Ob invariantnykh mnozhestvakh nekotorykh kvadratichnykh otobrazhenii ploskosti”, Vestn. Nizhegorodsk. un-ta. Ser. matem., 2012, no. 2(2), 152–158

[8] Katok A. B., Khasselblat B., Vvedenie v sovremennuyu teoriyu dinamicheskikh sistem, Faktorial, M., 1999

[9] Brin M., Pesin Ya., “On Morse–Smale endomorphisms”, American Math. Soc. Transl., 171:2 (1996), 35–45 | MR

[10] Azimov D., “Round handles and non-singular Morse–Smale flows”, Ann. Math., 102 (1975), 41–54 | DOI | MR

[11] Sharkovskii A. N., Maistrenko Yu. L., Romanenko E. Yu., Raznostnye uravneniya i ikh prilozheniya, Nauk. Dumka, Kiev, 1986 | MR

[12] Marsden Dzh., Mak-Kraken M., Bifurkatsiya rozhdeniya tsikla i ee prilozheniya, Mir, M., 1980 | MR | Zbl

[13] Andronov A. A., Leontovich E. A., Gordon I. I., Maier A. G., Kachestvennaya teoriya dinamicheskikh sistem vtorogo poryadka, Nauka, M., 1966 | MR | Zbl