Glyzin, S. D.; Kolesov, A. Yu. On some properties of the shift on an infinite-dimensional torus. (English. Russian original) Zbl 1527.37006 Differ. Equ. 59, No. 7, 867-879 (2023); translation from Differ. Uravn. 59, No. 7, 867-880 (2023). MSC: 37B05 58B25 PDFBibTeX XMLCite \textit{S. D. Glyzin} and \textit{A. Yu. Kolesov}, Differ. Equ. 59, No. 7, 867--879 (2023; Zbl 1527.37006); translation from Differ. Uravn. 59, No. 7, 867--880 (2023) Full Text: DOI
Glyzin, S. D.; Kolesov, A. Yu. Topologically mixing diffeomorphisms on the infinite-dimensional torus. (English. Russian original) Zbl 1522.37034 Math. Notes 113, No. 6, 859-863 (2023); translation from Mat. Zametki 113, No. 6, 929-934 (2023). MSC: 37C05 37D20 37D25 37A25 PDFBibTeX XMLCite \textit{S. D. Glyzin} and \textit{A. Yu. Kolesov}, Math. Notes 113, No. 6, 859--863 (2023; Zbl 1522.37034); translation from Mat. Zametki 113, No. 6, 929--934 (2023) Full Text: DOI
Glyzin, Sergey D.; Kolesov, Andrei Yu. Elements of hyperbolic theory on an infinite-dimensional torus. (English. Russian original) Zbl 1526.37033 Russ. Math. Surv. 77, No. 3, 379-443 (2022); translation from Usp. Mat. Nauk 77, No. 3, 3-72 (2022). MSC: 37D20 46T20 37E30 58B20 58B10 PDFBibTeX XMLCite \textit{S. D. Glyzin} and \textit{A. Yu. Kolesov}, Russ. Math. Surv. 77, No. 3, 379--443 (2022; Zbl 1526.37033); translation from Usp. Mat. Nauk 77, No. 3, 3--72 (2022) Full Text: DOI MNR
Glyzin, Sergei D.; Kolesov, Andrei Yu. A hyperbolicity criterion for a class of diffeomorphisms of an infinite-dimensional torus. (English. Russian original) Zbl 1510.37048 Sb. Math. 213, No. 2, 173-215 (2022); translation from Mat. Sb. 213, No. 2, 50-95 (2022). Reviewer: Jonas Deré (Leuven) MSC: 37D20 37C05 37C15 46T20 37E30 58B20 PDFBibTeX XMLCite \textit{S. D. Glyzin} and \textit{A. Yu. Kolesov}, Sb. Math. 213, No. 2, 173--215 (2022; Zbl 1510.37048); translation from Mat. Sb. 213, No. 2, 50--95 (2022) Full Text: DOI
Glyzin, S. D.; Kolesov, A. Yu. Hyperbolicity criterion for torus endomorphisms. (English. Russian original) Zbl 1492.37038 Math. Notes 111, No. 1, 147-151 (2022); translation from Mat. Zametki 111, No. 1, 134-139 (2022). MSC: 37D20 37D10 37C05 PDFBibTeX XMLCite \textit{S. D. Glyzin} and \textit{A. Yu. Kolesov}, Math. Notes 111, No. 1, 147--151 (2022; Zbl 1492.37038); translation from Mat. Zametki 111, No. 1, 134--139 (2022) Full Text: DOI
Glyzin, S. D.; Kolesov, A. Yu. On some modifications of Arnold’s cat map. (English. Russian original) Zbl 1493.37051 Dokl. Math. 104, No. 2, 242-246 (2021); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 500, 26-30 (2021). MSC: 37E30 37E35 PDFBibTeX XMLCite \textit{S. D. Glyzin} and \textit{A. Yu. Kolesov}, Dokl. Math. 104, No. 2, 242--246 (2021; Zbl 1493.37051); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 500, 26--30 (2021) Full Text: DOI
Glyzin, S. D.; Kolesov, A. Yu.; Rozov, N. Kh. On the existence and stability of an infinite-dimensional invariant torus. (English. Russian original) Zbl 1473.37026 Math. Notes 109, No. 4, 534-550 (2021); translation from Mat. Zametki 109, No. 4, 508-528 (2021). MSC: 37C20 37C75 37C05 PDFBibTeX XMLCite \textit{S. D. Glyzin} et al., Math. Notes 109, No. 4, 534--550 (2021; Zbl 1473.37026); translation from Mat. Zametki 109, No. 4, 508--528 (2021) Full Text: DOI
Glyzin, Sergey D.; Kolesov, Andrei Yu.; Rozov, Nikolai Kh. On a class of Anosov diffeomorphisms on the infinite-dimensional torus. (English. Russian original) Zbl 1469.37021 Izv. Math. 85, No. 2, 177-227 (2021); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 85, No. 2, 3-59 (2021). Reviewer: Martin Sambarino (Montevideo) MSC: 37D20 37C05 37C15 37C75 PDFBibTeX XMLCite \textit{S. D. Glyzin} et al., Izv. Math. 85, No. 2, 177--227 (2021; Zbl 1469.37021); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 85, No. 2, 3--59 (2021) Full Text: DOI
Glyzin, S. D.; Kolesov, A. Yu.; Rozov, N. Kh. Expansive endomorphisms on the infinite-dimensional torus. (English. Russian original) Zbl 1473.37024 Funct. Anal. Appl. 54, No. 4, 241-256 (2020); translation from Funkts. Anal. Prilozh. 54, No. 4, 17-36 (2020). MSC: 37C15 37C20 37D20 37D25 37A25 PDFBibTeX XMLCite \textit{S. D. Glyzin} et al., Funct. Anal. Appl. 54, No. 4, 241--256 (2020; Zbl 1473.37024); translation from Funkts. Anal. Prilozh. 54, No. 4, 17--36 (2020) Full Text: DOI
Glyzin, S. D.; Kolesov, A. Yu.; Rozov, N. Kh. One class of structurally stable endomorphisms on an infinite-dimensional torus. (English. Russian original) Zbl 1458.37040 Differ. Equ. 56, No. 10, 1382-1386 (2020); translation from Differ. Uravn. 56, No. 10, 1412-1416 (2020). Reviewer: Marta Macho Stadler (Leioa) MSC: 37C85 37E30 57S05 PDFBibTeX XMLCite \textit{S. D. Glyzin} et al., Differ. Equ. 56, No. 10, 1382--1386 (2020; Zbl 1458.37040); translation from Differ. Uravn. 56, No. 10, 1412--1416 (2020) Full Text: DOI
Kolesov, A. Yu.; Rozov, N. Kh.; Sadovnichii, V. A. On the hyperbolicity of toral endomorphisms. (English. Russian original) Zbl 1416.37033 Math. Notes 105, No. 2, 236-250 (2019); translation from Mat. Zametki 105, No. 2, 251-268 (2019). MSC: 37D20 37C05 PDFBibTeX XMLCite \textit{A. Yu. Kolesov} et al., Math. Notes 105, No. 2, 236--250 (2019; Zbl 1416.37033); translation from Mat. Zametki 105, No. 2, 251--268 (2019) Full Text: DOI
Kolesov, A. Yu.; Rozov, N. Kh.; Sadovnichii, V. A. Sufficient condition for the hyperbolicity of mappings of the torus. (English. Russian original) Zbl 1376.37070 Differ. Equ. 53, No. 4, 457-478 (2017); translation from Differ. Uravn. 53, No. 4, 465-486 (2017). MSC: 37D20 37E30 PDFBibTeX XMLCite \textit{A. Yu. Kolesov} et al., Differ. Equ. 53, No. 4, 457--478 (2017; Zbl 1376.37070); translation from Differ. Uravn. 53, No. 4, 465--486 (2017) Full Text: DOI
Glyzin, S. D.; Kolesov, A. Yu.; Rozov, N. Kh. Two-frequency self-oscillations in a FitzHugh-Nagumo neural network. (English. Russian original) Zbl 1397.34080 Comput. Math. Math. Phys. 57, No. 1, 106-121 (2017); translation from Zh. Vychisl. Mat. Mat. Fiz. 57, No. 1, 94-110 (2017). Reviewer: Klaus R. Schneider (Berlin) MSC: 34C60 92C20 92B20 34C45 34C46 34D20 34E15 PDFBibTeX XMLCite \textit{S. D. Glyzin} et al., Comput. Math. Math. Phys. 57, No. 1, 106--121 (2017; Zbl 1397.34080); translation from Zh. Vychisl. Mat. Mat. Fiz. 57, No. 1, 94--110 (2017) Full Text: DOI
Sadovnichii, V. A.; Kolesov, A. Yu.; Rozov, N. Kh. Parametric chaos in nonlinear flutter systems. (English. Russian original) Zbl 1312.34084 Dokl. Math. 89, No. 3, 382-386 (2014); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 456, No. 2, 150-154 (2014). Reviewer: Hao Wu (Nanjing) MSC: 34C46 37D45 34D10 34C45 34C23 34D45 34C28 PDFBibTeX XMLCite \textit{V. A. Sadovnichii} et al., Dokl. Math. 89, No. 3, 382--386 (2014; Zbl 1312.34084); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 456, No. 2, 150--154 (2014) Full Text: DOI
Kolesov, A. Yu; Mishchenko, E. F.; Rozov, N. Kh Multifrequency self-oscillations in two-dimensional lattices of coupled oscillators. (English. Russian original) Zbl 1222.35041 Izv. Math. 75, No. 3, 539-567 (2011); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 2011, No. 3, 97-126 (2011). MSC: 35B41 37B25 37D45 37L30 65N22 39A12 35L71 35L20 PDFBibTeX XMLCite \textit{A. Y. Kolesov} et al., Izv. Math. 75, No. 3, 539--567 (2011; Zbl 1222.35041); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 2011, No. 3, 97--126 (2011) Full Text: DOI
Kolesov, A. Yu.; Rozov, N. Kh. Dynamic effects associated with spatial discretization of nonlinear wave equations. (Russian, English) Zbl 1224.35246 Zh. Vychisl. Mat. Mat. Fiz. 49, No. 10, 1812-1826 (2009); translation in Comput. Math., Math. Phys. 49, No. 10, 1733-1747 (2009). MSC: 35L05 35L15 35B41 PDFBibTeX XMLCite \textit{A. Yu. Kolesov} and \textit{N. Kh. Rozov}, Zh. Vychisl. Mat. Mat. Fiz. 49, No. 10, 1812--1826 (2009; Zbl 1224.35246); translation in Comput. Math., Math. Phys. 49, No. 10, 1733--1747 (2009) Full Text: DOI
Glyzin, S. D.; Kolesov, A. Yu.; Rozov, N. Kh. The question of the realizability of the Landau scenario for the development of turbulence. (English. Russian original) Zbl 1278.76033 Theor. Math. Phys. 158, No. 2, 246-261 (2009); translation from Teor. Mat. Fiz. 158, No. 2, 292-311 (2009). MSC: 76F20 76F02 37N10 35L71 37L10 37L30 PDFBibTeX XMLCite \textit{S. D. Glyzin} et al., Theor. Math. Phys. 158, No. 2, 246--261 (2009; Zbl 1278.76033); translation from Teor. Mat. Fiz. 158, No. 2, 292--311 (2009) Full Text: DOI
Kolesov, A. Yu.; Rosov, N. Kh. Two-frequency autowave processes in the complex Ginzburg-Landau equation. (English) Zbl 1178.35349 Theor. Math. Phys. 134, No. 3, 308-325 (2003); translation from Teor. Mat. Fiz. 134, No. 3, 353-373 (2003). MSC: 35Q55 76B15 76E30 PDFBibTeX XMLCite \textit{A. Yu. Kolesov} and \textit{N. Kh. Rosov}, Theor. Math. Phys. 134, No. 3, 308--325 (2003; Zbl 1178.35349); translation from Teor. Mat. Fiz. 134, No. 3, 353--373 (2003) Full Text: DOI
Kolesov, A. Yu.; Kolesov, Yu. S.; Rozov, N. Kh. Chaos of ‘split torus’ type in three-dimensional relaxation systems. (English. Russian original) Zbl 0904.34040 Sb. Math. 188, No. 11, 1571-1586 (1997); translation from Sb. 188, No. 11, 3-18 (1997). MSC: 34C30 34C15 34C05 PDFBibTeX XMLCite \textit{A. Yu. Kolesov} et al., Sb. Math. 188, No. 11, 1571--1586 (1997; Zbl 0904.34040); translation from Sb. 188, No. 11, 3--18 (1997) Full Text: DOI
Kolesov, A. Yu.; Kolesov, Yu. S.; Rozov, N. Kh. Chaos of broken torus type in three-dimensional relaxation systems. (English) Zbl 0872.34031 J. Math. Sci., New York 80, No. 1, 1533-1545 (1996). Reviewer: C.Mira (Toulouse) MSC: 37C70 34C15 PDFBibTeX XMLCite \textit{A. Yu. Kolesov} et al., J. Math. Sci., New York 80, No. 1, 1533--1545 (1996; Zbl 0872.34031) Full Text: DOI
Kolesov, A. Yu. On the existence and stability of a two-dimensional relaxational torus. (English. Russian original) Zbl 0835.34068 Math. Notes 56, No. 6, 1238-1243 (1994); translation from Mat. Zametki 56, No. 6, 40-47 (1994). MSC: 34E15 34C15 34C30 PDFBibTeX XMLCite \textit{A. Yu. Kolesov}, Math. Notes 56, No. 6, 1238--1243 (1994; Zbl 0835.34068); translation from Mat. Zametki 56, No. 6, 40--47 (1994) Full Text: DOI
Kolesov, A. Yu.; Mishchenko, E. F. On the mechanism of collapse of the invariant torus of the van der Pol relaxation system with harmonic action on the slow variable. (English. Russian original) Zbl 0786.34053 Proc. Steklov Inst. Math. 200, 219-226 (1993); translation from Tr. Mat. Inst. Steklova 200, 197-204 (1991). MSC: 34C45 34D15 34C25 34C30 34E15 PDFBibTeX XMLCite \textit{A. Yu. Kolesov} and \textit{E. F. Mishchenko}, in: Number theory, algebra, mathematical analysis and their applications. Dedicated to the 100th anniversary of the birth of Ivan Matveevich Vinogradov. Providence, RI: American Mathematical Society. 219--226 (1991; Zbl 0786.34053); translation from Tr. Mat. Inst. Steklova 200, 197--204 (1991)
Kolesov, A. Yu.; Mishchenko, E. F. Existence and stability of the relaxation torus. (English. Russian original) Zbl 0704.34003 Russ. Math. Surv. 44, No. 3, 204-205 (1989); translation from Usp. Mat. Nauk 44, No. 3(267), 161-162 (1989). Reviewer: Yu.N.Bibikov MSC: 34A12 34D20 PDFBibTeX XMLCite \textit{A. Yu. Kolesov} and \textit{E. F. Mishchenko}, Russ. Math. Surv. 44, No. 3, 204--205 (1989; Zbl 0704.34003); translation from Usp. Mat. Nauk 44, No. 3(267), 161--162 (1989) Full Text: DOI