groups of gomeomorphisms of local-compact space; metric invariants of groups of transformations; the functional-differential equations; deviating argument; the principle of maximum.
Main publications:
Beklaryan L. A. Zadacha optimalnogo upravleniya dlya sistem s otklonyayuschimsya argumentom i ee svyaz s konechno-porozhdennoi gruppoi gomeomorfizmov $\mathbb R$, porozhdennoi funktsiyami otkloneniya // DAN SSSR, 1991, 317(6), 1289–1294.
Beklaryan L. A. Gruppovye osobennosti differentsialnykh uravnenii s otklonyayuschimsya argumentom. Vvedenie v lineinuyu teoriyu // Matem. zametki, 1998, 63(4), 483–493.
Beklaryan L. A. K voprosu o klassifikatsii grupp gomeomorfizmov $\mathbb R$, sokhranyayuschikh orientatsiyu. I. Invariantnye mery // Matem. sbornik, 1996, 187(3), 22–54.
Beklaryan L. A. K voprosu o klassifikatsii grupp gomeomorfizmov $\mathbb R$, sokhranyayuschikh orientatsiyu. II. Proektivno-invariantnye mery // Matem. sbornik, 1996, 187(4), 3–28.
Beklaryan L. A. K voprosu o klassifikatsii grupp gomeomorfizmov $\mathbb R$, sokhranyayuschikh orientatsiyu // Matem. sbornik, 190(4), 43–62.
A. L. Beklaryan, L. A. Beklaryan, “Existence of bounded soliton solutions in the problem of longitudinal oscillations of an elastic infinite rod in a field with a nonlinear potential of general form”, Zh. Vychisl. Mat. Mat. Fiz., 62:6 (2022), 933–950; Comput. Math. Math. Phys., 62:6 (2022), 904–919
L. A. Beklaryan, A. L. Beklaryan, “Existence of bounded soliton solutions in the problem of longitudinal vibrations of an infinite elastic rod in a field with a strongly nonlinear potential”, Zh. Vychisl. Mat. Mat. Fiz., 61:12 (2021), 2024–2039; Comput. Math. Math. Phys., 61:12 (2021), 1980–1994
L. A. Beklaryan, “A new approach to the question of the existence of bounded solutions of functional differential equations of
point type”, Izv. RAN. Ser. Mat., 84:2 (2020), 3–42; Izv. Math., 84:2 (2020), 209–245
L. A. Beklaryan, A. L. Beklaryan, “Functional differential equations of pointwise type: bifurcation”, Zh. Vychisl. Mat. Mat. Fiz., 60:8 (2020), 1291–1303; Comput. Math. Math. Phys., 60:8 (2020), 1249–1260
2019
6.
L. A. Beklaryan, “On massive subsets in the space of finitely generated groups of diffeomorphisms of the line and the circle in the case of $C^{(1)}$ smoothness”, Fundam. Prikl. Mat., 22:4 (2019), 51–74; J. Math. Sci., 257:6 (2021), 780–796
7.
L. A. Beklaryan, “Groups of line and circle homeomorphisms. Criteria for almost nilpotency”, Mat. Sb., 210:4 (2019), 27–40; Sb. Math., 210:4 (2019), 495–507
2018
8.
L. A. Beklaryan, “A new approach to the question of existence of periodic solutions
for functional differential equations of point type”, Izv. RAN. Ser. Mat., 82:6 (2018), 3–36; Izv. Math., 82:6 (2018), 1077–1107
L. A. Beklaryan, “Groups of line and circle diffeomorphisms. Criteria for almost nilpotency and structure theorems”, Mat. Sb., 207:8 (2016), 47–72; Sb. Math., 207:8 (2016), 1079–1099
A. S. Akopov, L. A. Beklaryan, “An agent model of crowd behavior in emergencies”, Avtomat. i Telemekh., 2015, no. 10, 131–143; Autom. Remote Control, 76:10 (2015), 1817–1827
L. A. Beklaryan, “Groups of line and circle homeomorphisms. Metric invariants and questions of classification”, Uspekhi Mat. Nauk, 70:2(422) (2015), 3–54; Russian Math. Surveys, 70:2 (2015), 203–248
A. S. Akopov, L. A. Beklaryan, A. L. Beklaryan, A. K. Saghatelyan, “The integrated model of eco-economic system on the example of the Republic of Armenia”, Computer Research and Modeling, 6:4 (2014), 621–631
L. A. Beklaryan, “Criteria for the Existence of an Invariant Measure for Groups of Homeomorphisms of the Line”, Mat. Zametki, 95:3 (2014), 335–339; Math. Notes, 95:3 (2014), 304–307
L. A. Beklaryan, “Groups of homeomorphisms of the line. Criteria for the existence of invariant and projectively invariant measures in terms of the commutator subgroup”, Mat. Sb., 205:12 (2014), 63–84; Sb. Math., 205:12 (2014), 1741–1760
L. A. Beklaryan, N. K. Khachatryan, “On one class of dynamic transportation models”, Zh. Vychisl. Mat. Mat. Fiz., 53:10 (2013), 1649–1667; Comput. Math. Math. Phys., 53:10 (2013), 1466–1482
L. A. Beklaryan, “Residual Subsets in the Space of Finitely Generated Groups of Diffeomorphisms of the Circle”, Mat. Zametki, 92:6 (2012), 825–833; Math. Notes, 93:1 (2013), 29–35
L. A. Beklaryan, S. V. Borisova, N. K. Khachatryan, “A single-dynamic model of replacement assets. Main properties”, Zh. Vychisl. Mat. Mat. Fiz., 52:5 (2012), 801–817
L. A. Beklaryan, “The linear theory of functional differential equations: existence theorems and the problem of pointwise completeness of the solutions”, Mat. Sb., 202:3 (2011), 3–36; Sb. Math., 202:3 (2011), 307–340
L. A. Beklaryan, “The structure of a group quasisymmetrically conjugate to a group of affine transformations of the real line”, Mat. Sb., 196:10 (2005), 3–20; Sb. Math., 196:10 (2005), 1403–1420
2004
21.
L. A. Beklaryan, “Introduction to the theory of functional differential equations and their applications. Group approach”, CMFD, 8 (2004), 3–147; Journal of Mathematical Sciences, 135:2 (2006), 2813–2954
L. A. Beklaryan, “Groups of homeomorphisms of the line and the circle.
Topological characteristics and metric invariants”, Uspekhi Mat. Nauk, 59:4(358) (2004), 3–68; Russian Math. Surveys, 59:4 (2004), 599–660
L. A. Beklaryan, “Equations of Advanced–Retarded Type and Solutions of Traveling-Wave Type for Infinite-Dimensional Dynamic Systems”, CMFD, 1 (2003), 18–29; Journal of Mathematical Sciences, 124:4 (2004), 5098–5109
L. A. Beklaryan, “On Analogs of the Tits Alternative for Groups of Homeomorphisms of the Circle and of the Line”, Mat. Zametki, 71:3 (2002), 334–347; Math. Notes, 71:3 (2002), 305–315
L. A. Beklaryan, “On a criterion for the topological conjugacy of a quasisymmetric group to a group of affine transformations of $\mathbb R$”, Mat. Sb., 191:6 (2000), 31–42; Sb. Math., 191:6 (2000), 809–819
L. A. Beklaryan, “Group singularities of differential equations with deviating argument, and related metric invariants”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 67 (1999), 161–182; J. Math. Sci. (New York), 105:1 (2001), 1799–1811
L. A. Beklaryan, “On the classification of groups of orientation-preserving homeomorphisms of $\mathbb R$. III. $\omega$-projectively invariant measures”, Mat. Sb., 190:4 (1999), 43–62; Sb. Math., 190:4 (1999), 521–538
L. A. Beklaryan, “Specific group properties of differential equations with deviating argument. Introduction to the linear theory”, Mat. Zametki, 63:4 (1998), 483–493; Math. Notes, 63:4 (1998), 427–435
L. A. Beklaryan, “A criterion connected with the structure of the fixed-point set for the existence of a projectively invariant measure for groups of orientation-preserving homeomorphisms of $\mathbb R$”, Uspekhi Mat. Nauk, 51:3(309) (1996), 179–180; Russian Math. Surveys, 51:3 (1996), 539–540
L. A. Beklaryan, “On the classification of groups of orientation-preserving homeomorphisms of $\mathbb R$.
II. Projectively-invariant measures”, Mat. Sb., 187:4 (1996), 3–28; Sb. Math., 187:4 (1996), 469–494
L. A. Beklaryan, “On the classification of groups of orientation-preserving homeomorphisms of $\mathbb R$.
I. Invariant measures”, Mat. Sb., 187:3 (1996), 23–54; Sb. Math., 187:3 (1996), 335–364
L. A. Beklaryan, M. G. Shmul'yan, “On the completeness of solutions of a differential equation with
deviating argument that are majorized by exponential functions”, Dokl. Akad. Nauk, 341:6 (1995), 727–730
L. A. Beklaryan, “On the theory of linear differential-delay equations”, Uspekhi Mat. Nauk, 49:6(300) (1994), 193–194; Russian Math. Surveys, 49:6 (1994), 197–198
L. A. Beklaryan, “Invariant and projectively invariant measures for groups of orientation-preserving homeomorphisms of $\mathbb{R}$”, Dokl. Akad. Nauk, 332:6 (1993), 679–681; Dokl. Math., 48:2 (1994), 387–390
L. A. Beklaryan, “The structure of the quotient group of the group of orientation-preserving homeomorphisms of $\mathbb{R}$ by the subgroup generated by the union of the stabilizers”, Dokl. Akad. Nauk, 331:2 (1993), 137–139; Dokl. Math., 48:1 (1994), 37–39
L. A. Beklaryan, “An optimal control problem for systems with deviating argument and
its connection with the finitely generated group of homeomorphisms $R$
generated by deviation functions”, Dokl. Akad. Nauk SSSR, 317:6 (1991), 1289–1294; Dokl. Math., 43:2 (1991), 600–605
L. A. Beklaryan, “A method for the regularization of boundary value problems for
differential equations with deviating argument”, Dokl. Akad. Nauk SSSR, 317:5 (1991), 1033–1037; Dokl. Math., 43:2 (1991), 567–571
L. A. Beklaryan, “Reducibility of a differential equation with deviating argument to an equation with commensurable constant deviations”, Mat. Zametki, 44:5 (1988), 561–566; Math. Notes, 44:5 (1988), 787–789
L. A. Beklaryan, “A variational problem with retarded argument and its relation to
some semigroup of mappings of a segment into itself”, Dokl. Akad. Nauk SSSR, 271:5 (1983), 1036–1040
E. R. Avakov, A. V. Arutyunov, L. A. Beklaryan, È. M. Galeev, M. L. Gol'dman, V. B. Demidovich, A. G. Kusraev, G. G. Magaril-Il'yaev, V. M. Tikhomirov, “Osipenko Konstantin Yur'evich (on his 60th birthday)”, Vladikavkaz. Mat. Zh., 12:1 (2010), 68–70
Presentations in Math-Net.Ru
1.
Dualism in the theory of soliton solutions L. A. Beklaryan, A. L. Beklaryan The ninth international conference "Quasilinear Equations, Inverse Problems and their Applications" (QIPA 2023) December 5, 2023 16:15
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