Grines, V. Z.; Gurevich, E. Ya. A combinatorial invariant of gradient-like flows on a connected sum of \(\mathbb{S}^{n-1}\times\mathbb{S}^1\). (English. Russian original) Zbl 07787327 Sb. Math. 214, No. 5, 703-731 (2023); translation from Mat. Sb. 214, No. 5, 97-127 (2023). MSC: 37C15 37C20 37B35 37B25 37B30 37C75 37E15 PDFBibTeX XMLCite \textit{V. Z. Grines} and \textit{E. Ya. Gurevich}, Sb. Math. 214, No. 5, 703--731 (2023; Zbl 07787327); translation from Mat. Sb. 214, No. 5, 97--127 (2023) Full Text: DOI MNR
Barinova, Marina; Grines, Vyacheslav; Pochinka, Olga Dynamics of three-dimensional \(\mathrm{A}\)-diffeomorphisms with two-dimensional attractors and repellers. (English) Zbl 07775583 J. Difference Equ. Appl. 29, No. 9-12, 1275-1286 (2023). MSC: 37C70 37C20 37C05 PDFBibTeX XMLCite \textit{M. Barinova} et al., J. Difference Equ. Appl. 29, No. 9--12, 1275--1286 (2023; Zbl 07775583) Full Text: DOI
Grines, V. Z.; Mints, D. I.; Chilina, E. E. Perturbations of nonhyperbolic algebraic automorphisms of the 2-torus. (English. Russian original) Zbl 07761818 Math. Notes 114, No. 2, 187-198 (2023); translation from Mat. Zametki 114, No. 2, 229-243 (2023). MSC: 37C20 37C15 37C27 37C29 37D15 37E30 PDFBibTeX XMLCite \textit{V. Z. Grines} et al., Math. Notes 114, No. 2, 187--198 (2023; Zbl 07761818); translation from Mat. Zametki 114, No. 2, 229--243 (2023) Full Text: DOI
Baranov, Denis A.; Grines, Vyacheslav Z.; Pochinka, Olga V.; Chilina, Ekaterina E. On a classification of periodic maps on the 2-torus. (English) Zbl 1528.37035 Russ. J. Nonlinear Dyn. 19, No. 1, 91-110 (2023). MSC: 37E30 37C27 37C29 37C15 37C20 37C05 PDFBibTeX XMLCite \textit{D. A. Baranov} et al., Russ. J. Nonlinear Dyn. 19, No. 1, 91--110 (2023; Zbl 1528.37035) Full Text: DOI arXiv MNR
Barinova, M. K.; Grines, V. Z.; Pochinka, O. V. Criterion for the existence of an energy function for a regular homeomorphism of the 3-sphere. (English. Russian original) Zbl 1527.37019 Proc. Steklov Inst. Math. 321, 37-53 (2023); translation from Tr. Mat. Inst. Steklova 321, 45-61 (2023). MSC: 37C15 37C20 37C75 37C05 PDFBibTeX XMLCite \textit{M. K. Barinova} et al., Proc. Steklov Inst. Math. 321, 37--53 (2023; Zbl 1527.37019); translation from Tr. Mat. Inst. Steklova 321, 45--61 (2023) Full Text: DOI
Grines, Vyacheslav Z.; Mints, Dmitrii I. On partially hyperbolic diffeomorphisms and regular Denjoy type homeomorphisms. (English) Zbl 07720900 Regul. Chaotic Dyn. 28, No. 3, 295-308 (2023). Reviewer: Martin Sambarino (Montevideo) MSC: 37E30 37D30 37C15 37C20 PDFBibTeX XMLCite \textit{V. Z. Grines} and \textit{D. I. Mints}, Regul. Chaotic Dyn. 28, No. 3, 295--308 (2023; Zbl 07720900) Full Text: DOI
Grines, Vyacheslav; Morozov, Andrei; Pochinka, Olga Determination of the homotopy type of a Morse-Smale diffeomorphism on an orientable surface by a heteroclinic intersection. (English) Zbl 1521.37022 Qual. Theory Dyn. Syst. 22, No. 3, Paper No. 120, 12 p. (2023). MSC: 37C20 37C15 37C05 PDFBibTeX XMLCite \textit{V. Grines} et al., Qual. Theory Dyn. Syst. 22, No. 3, Paper No. 120, 12 p. (2023; Zbl 1521.37022) Full Text: DOI
Grines, V. Z.; Pochinka, O. V.; Chilina, E. E. Dynamics of 3-homeomorphisms with two-dimensional attractors and repellers. (English. Russian original) Zbl 1516.37028 J. Math. Sci., New York 270, No. 5, 683-692 (2023); translation from Probl. Mat. Anal. 123, 57-65 (2023). MSC: 37C15 37C20 37C70 PDFBibTeX XMLCite \textit{V. Z. Grines} et al., J. Math. Sci., New York 270, No. 5, 683--692 (2023; Zbl 1516.37028); translation from Probl. Mat. Anal. 123, 57--65 (2023) Full Text: DOI
Grines, V. Z.; Mints, D. I. On one-dimensional contracting repellers of \(A\)-endomorphisms of the 2-torus. (English. Russian original) Zbl 1516.37027 Math. Notes 113, No. 4, 593-597 (2023); translation from Mat. Zametki 113, No. 4, 613-617 (2023). MSC: 37C15 37C20 37C70 37E30 37E35 PDFBibTeX XMLCite \textit{V. Z. Grines} and \textit{D. I. Mints}, Math. Notes 113, No. 4, 593--597 (2023; Zbl 1516.37027); translation from Mat. Zametki 113, No. 4, 613--617 (2023) Full Text: DOI
Grines, Vyacheslav Z.; Medvedev, Vladislav S.; Zhuzhoma, Evgeny V. On the topological structure of manifolds supporting axiom a systems. (English) Zbl 1517.37034 Regul. Chaotic Dyn. 27, No. 6, 613-628 (2022). MSC: 37D15 37C20 37C15 37C25 37C27 37C29 PDFBibTeX XMLCite \textit{V. Z. Grines} et al., Regul. Chaotic Dyn. 27, No. 6, 613--628 (2022; Zbl 1517.37034) Full Text: DOI
Grines, Vyacheslav Zigmundovich; Mints, Dmitriĭ Il’ich; Chilina, Ekaterina Evgen’evna On perturbations of algebraic periodic automorphisms of a two-dimensional torus. (Russian. English summary) Zbl 1524.37042 Zh. Sredn. Mat. Obshch. 24, No. 2, 141-150 (2022). MSC: 37E30 37C05 37C15 37C20 57R50 58C25 PDFBibTeX XMLCite \textit{V. Z. Grines} et al., Zh. Sredn. Mat. Obshch. 24, No. 2, 141--150 (2022; Zbl 1524.37042) Full Text: DOI MNR
Grines, V. Z.; Gurevich, E. Ya.; Pochinka, O. V. On embedding of the Morse-Smale diffeomorphisms in a topological flow. (English. Russian original) Zbl 1507.37037 J. Math. Sci., New York 265, No. 6, 868-887 (2022); translation from Sovrem. Mat., Fundam. Napravl. 66, No. 2, 160-181 (2020). MSC: 37D15 37C20 37C15 PDFBibTeX XMLCite \textit{V. Z. Grines} et al., J. Math. Sci., New York 265, No. 6, 868--887 (2022; Zbl 1507.37037); translation from Sovrem. Mat., Fundam. Napravl. 66, No. 2, 160--181 (2020) Full Text: DOI
Grines, V. Z.; Mints, D. I. On topological classification of regular Denjoy type homeomorphisms. (English. Russian original) Zbl 1523.37050 Dokl. Math. 106, No. 1, 268-271 (2022); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 505, 66-70 (2022). Reviewer: Francisco Balibrea (Murcia) MSC: 37E30 37E10 37E45 37C15 37C20 PDFBibTeX XMLCite \textit{V. Z. Grines} and \textit{D. I. Mints}, Dokl. Math. 106, No. 1, 268--271 (2022; Zbl 1523.37050); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 505, 66--70 (2022) Full Text: DOI
Grines, V. Z.; Lerman, L. M. Nonautonomous vector fields on \(S^3\): simple dynamics and wild embedding of separatrices. (English. Russian original) Zbl 1516.37030 Theor. Math. Phys. 212, No. 1, 903-917 (2022); translation from Teor. Mat. Fiz. 212, No. 1, 15-32 (2022). MSC: 37C60 37C10 37C05 37C20 37C15 37C65 PDFBibTeX XMLCite \textit{V. Z. Grines} and \textit{L. M. Lerman}, Theor. Math. Phys. 212, No. 1, 903--917 (2022; Zbl 1516.37030); translation from Teor. Mat. Fiz. 212, No. 1, 15--32 (2022) Full Text: DOI arXiv
Grines, Vyacheslav; Mints, Dmitrii On decomposition of ambient surfaces admitting \(A\)-diffeomorphisms with non-trivial attractors and repellers. (English) Zbl 1498.37051 Discrete Contin. Dyn. Syst. 42, No. 7, 3557-3568 (2022). MSC: 37D20 37C05 37C15 37C20 37C70 37D40 PDFBibTeX XMLCite \textit{V. Grines} and \textit{D. Mints}, Discrete Contin. Dyn. Syst. 42, No. 7, 3557--3568 (2022; Zbl 1498.37051) Full Text: DOI arXiv
Grines, V. Z.; Gurevich, E. Ya. Morse index of saddle equilibria of gradient-like flows on connected sums of \(\mathbb{S}^{n-1}\times \mathbb{S}^1\). (English. Russian original) Zbl 1497.37027 Math. Notes 111, No. 4, 624-627 (2022); translation from Mat. Zametki 111, No. 4, 616-619 (2022). MSC: 37C15 37C20 37C75 37B35 37B25 37B30 PDFBibTeX XMLCite \textit{V. Z. Grines} and \textit{E. Ya. Gurevich}, Math. Notes 111, No. 4, 624--627 (2022; Zbl 1497.37027); translation from Mat. Zametki 111, No. 4, 616--619 (2022) Full Text: DOI
Grines, V. Z.; Kruglov, E. V.; Pochinka, O. V. On the topological classification of structurally stable diffeomorphisms on 3-manifolds with a 2-dimensional expanding attractor. (English) Zbl 1496.37020 Lobachevskii J. Math. 42, No. 14, 3372-3381 (2021). MSC: 37C20 37C75 37C70 37C05 PDFBibTeX XMLCite \textit{V. Z. Grines} et al., Lobachevskii J. Math. 42, No. 14, 3372--3381 (2021; Zbl 1496.37020) Full Text: DOI
Grines, V. Z.; Morozov, A. I.; Pochinka, O. V. Realization of homeomorphisms of surfaces of algebraically finite order by Morse-Smale diffeomorphisms with orientable heteroclinic intersection. (English. Russian original) Zbl 1487.37026 Proc. Steklov Inst. Math. 315, 85-97 (2021); translation from Tr. Mat. Inst. Steklova 315, 95-107 (2021). MSC: 37C20 37C15 37C05 37C29 37E30 37D15 58C25 57R50 PDFBibTeX XMLCite \textit{V. Z. Grines} et al., Proc. Steklov Inst. Math. 315, 85--97 (2021; Zbl 1487.37026); translation from Tr. Mat. Inst. Steklova 315, 95--107 (2021) Full Text: DOI
Grines, Vyacheslav; Mints, Dmitrii On interrelations between trivial and nontrivial basic sets of structurally stable diffeomorphisms of surfaces. (English) Zbl 1466.37020 Chaos 31, No. 2, 023132, 7 p. (2021). Reviewer: William J. Satzer Jr. (St. Paul) MSC: 37C20 37C75 37C05 37C25 37C70 37E30 PDFBibTeX XMLCite \textit{V. Grines} and \textit{D. Mints}, Chaos 31, No. 2, 023132, 7 p. (2021; Zbl 1466.37020) Full Text: DOI
Grines, V. Z.; Gurevich, E. Ya.; Medvedev, V. S. On realization of topological conjugacy classes of Morse-Smale cascades on the sphere \(S^n\). (English. Russian original) Zbl 1456.37027 Proc. Steklov Inst. Math. 310, 108-123 (2020); translation from Tr. Mat. Inst. Steklova 310, 119-134 (2020). MSC: 37C15 37C20 37C05 37D15 PDFBibTeX XMLCite \textit{V. Z. Grines} et al., Proc. Steklov Inst. Math. 310, 108--123 (2020; Zbl 1456.37027); translation from Tr. Mat. Inst. Steklova 310, 119--134 (2020) Full Text: DOI
Grines, V. Z.; Pochinka, O. V. The constructing of energy functions for \(\Omega \)-stable diffeomorphisms on 2- and 3-manifolds. (English. Russian original) Zbl 1452.37024 J. Math. Sci., New York 250, No. 4, 537-568 (2020); translation from Sovrem. Mat., Fundam. Napravl. 63, No. 2, 191-222 (2017). Reviewer: William J. Satzer Jr. (St. Paul) MSC: 37C20 37C15 37C05 37C75 PDFBibTeX XMLCite \textit{V. Z. Grines} and \textit{O. V. Pochinka}, J. Math. Sci., New York 250, No. 4, 537--568 (2020; Zbl 1452.37024); translation from Sovrem. Mat., Fundam. Napravl. 63, No. 2, 191--222 (2017) Full Text: DOI
Grines, V. Z.; Kruglov, E. V.; Pochinka, O. V. Scenario of a simple transition from a structurally stable 3-diffeomorphism with a two-dimensional expanding attractor to a DA diffeomorphism. (English. Russian original) Zbl 1445.37018 Proc. Steklov Inst. Math. 308, 141-154 (2020); translation from Tr. Mat. Inst. Steklova 308, 152-166 (2020). Reviewer: Ivan Podvigin (Novosibirsk) MSC: 37C20 37C05 37C70 37C75 37G10 37G35 PDFBibTeX XMLCite \textit{V. Z. Grines} et al., Proc. Steklov Inst. Math. 308, 141--154 (2020; Zbl 1445.37018); translation from Tr. Mat. Inst. Steklova 308, 152--166 (2020) Full Text: DOI
Grines, Vyacheslav Z.; Kruglov, Evgeniy V.; Medvedev, Timur V.; Pochinka, Olga V. On embedding of arcs and circles in 3-manifolds and its application to dynamics of structurally stable 3-diffeomorhisms with two-dimensional expanding attractors. (English) Zbl 1437.37026 Topology Appl. 271, Article ID 106989, 10 p. (2020). Reviewer: Thomas B. Ward (Leeds) MSC: 37C20 37C05 37D15 37C70 37C75 PDFBibTeX XMLCite \textit{V. Z. Grines} et al., Topology Appl. 271, Article ID 106989, 10 p. (2020; Zbl 1437.37026) Full Text: DOI
Grines, V.; Gurevich, E.; Pochinka, O. On embedding of multidimensional Morse-Smale diffeomorphisms into topological flows. (English) Zbl 1460.37019 Mosc. Math. J. 19, No. 4, 739-760 (2019). MSC: 37C05 37C15 37C20 37D15 54C25 PDFBibTeX XMLCite \textit{V. Grines} et al., Mosc. Math. J. 19, No. 4, 739--760 (2019; Zbl 1460.37019) Full Text: arXiv Link
Grines, V. Z.; Gurevich, E. Ya.; Zhuzhoma, E. V.; Pochinka, O. V. Classification of Morse-Smale systems and topological structure of the underlying manifolds. (English. Russian original) Zbl 1444.37002 Russ. Math. Surv. 74, No. 1, 37-110 (2019); translation from Usp. Mat. Nauk 74, No. 1, 41-116 (2019). Reviewer: Igor V. Nikolaev (New York) MSC: 37-02 37C15 37D15 37C20 PDFBibTeX XMLCite \textit{V. Z. Grines} et al., Russ. Math. Surv. 74, No. 1, 37--110 (2019; Zbl 1444.37002); translation from Usp. Mat. Nauk 74, No. 1, 41--116 (2019) Full Text: DOI
Grines, V. Z.; Kurenkov, E. D. Representation of spaciously situated perfect attractors of diffeomorphisms by geodesic laminations. (Russian. English summary) Zbl 1449.37021 Zh. Sredn. Mat. Obshch. 20, No. 2, 159-174 (2018). Reviewer: Artyom Andronov (Saransk) MSC: 37C70 37C05 37C20 37C15 PDFBibTeX XMLCite \textit{V. Z. Grines} and \textit{E. D. Kurenkov}, Zh. Sredn. Mat. Obshch. 20, No. 2, 159--174 (2018; Zbl 1449.37021) Full Text: DOI
Grines, V.; Levchenko, Yu; Medvedev, V.; Pochinka, O. The topological classification of structurally stable 3-diffeomorphisms with two-dimensional basic sets. (English) Zbl 1357.37029 Nonlinearity 28, No. 11, 4081-4102 (2015). MSC: 37C15 37C05 PDFBibTeX XMLCite \textit{V. Grines} et al., Nonlinearity 28, No. 11, 4081--4102 (2015; Zbl 1357.37029) Full Text: DOI Link
Grines, Vyacheslav Z.; Levchenko, Yulia A.; Medvedev, Vladislav S.; Pochinka, Olga V. On the dynamical coherence of structurally stable 3-diffeomorphisms. (English) Zbl 1335.37010 Regul. Chaotic Dyn. 19, No. 4, 506-512 (2014). MSC: 37D20 37D30 37C75 PDFBibTeX XMLCite \textit{V. Z. Grines} et al., Regul. Chaotic Dyn. 19, No. 4, 506--512 (2014; Zbl 1335.37010) Full Text: DOI
Grines, V. Z.; Levchenko, Yu. A. On a topological classification of diffeomorphisms on 3-manifolds with two-dimensional surface attractors and repellers. (English. Russian summary) Zbl 1283.37039 Dokl. Math. 86, No. 3, 747-749 (2012); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 447, No. 2, 127-129 (2012). Reviewer: José A. Langa (Sevilla) MSC: 37D20 37C70 PDFBibTeX XMLCite \textit{V. Z. Grines} and \textit{Yu. A. Levchenko}, Dokl. Math. 86, No. 3, 747--749 (2012; Zbl 1283.37039); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 447, No. 2, 127--129 (2012) Full Text: DOI
Grines, V.; Zhuzhoma, E. On structurally stable diffeomorphisms with codimension one expanding attractors. (English) Zbl 1070.37012 Trans. Am. Math. Soc. 357, No. 2, 617-667 (2005). Reviewer: Messoud A. Efendiev (Berlin) MSC: 37C20 37D20 37C70 37C15 PDFBibTeX XMLCite \textit{V. Grines} and \textit{E. Zhuzhoma}, Trans. Am. Math. Soc. 357, No. 2, 617--667 (2005; Zbl 1070.37012) Full Text: DOI
Grines, V. Z.; Zhuzhoma, E. V. Structurally stable diffeomorphisms with basis sets of codimension one. (English. Russian original) Zbl 1017.37010 Izv. Math. 66, No. 2, 223-284 (2002); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 66, No. 2, 3-66 (2002). Reviewer: Yuri V.Rogovchenko (Famagusta) MSC: 37C15 37C70 37C20 37D20 37C27 PDFBibTeX XMLCite \textit{V. Z. Grines} and \textit{E. V. Zhuzhoma}, Izv. Math. 66, No. 2, 223--284 (2002; Zbl 1017.37010); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 66, No. 2, 3--66 (2002) Full Text: DOI
Bonatti, C.; Grines, V.; Langevin, R. Dynamical systems in dimension 2 and 3: conjugacy invariants and classification. (English) Zbl 1121.37306 Comput. Appl. Math. 20, No. 1-2, 11-50 (2001). MSC: 37C10 37D15 37C15 37E20 37C20 PDFBibTeX XMLCite \textit{C. Bonatti} et al., Comput. Appl. Math. 20, No. 1--2, 11--50 (2001; Zbl 1121.37306)
Grines, V. Z.; Zhuzhoma, E. V. On structurally stable diffeomorphisms with expanding attractors or contracting repellers of codimension one. (English. Russian original) Zbl 1041.37009 Dokl. Math. 62, No. 2, 274-276 (2000); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 374, No. 6, 735-737 (2000). Reviewer: Yuri V. Rogovchenko (Famagusta) MSC: 37C70 37C20 37D20 PDFBibTeX XMLCite \textit{V. Z. Grines} and \textit{E. V. Zhuzhoma}, Dokl. Math. 62, No. 2, 735--737 (2000; Zbl 1041.37009); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 374, No. 6, 735--737 (2000)
Bonatti, C.; Grines, V. Knots as topological invariants for gradient-like diffeomorphisms of the sphere \(S^3\). (English) Zbl 0959.37017 J. Dyn. Control Syst. 6, No. 4, 579-602 (2000). Reviewer: Athanase Papadopoulos (Strasbourg) MSC: 37C15 37B35 34D30 PDFBibTeX XMLCite \textit{C. Bonatti} and \textit{V. Grines}, J. Dyn. Control Syst. 6, No. 4, 579--602 (2000; Zbl 0959.37017) Full Text: DOI
Grines, V. Z. On topological classification of \(A\)-diffeomorphisms of surfaces. (English) Zbl 0984.37020 J. Dyn. Control Syst. 6, No. 1, 97-126 (2000). Reviewer: Messoud Efendiev (Berlin) MSC: 37C15 37D15 37E30 37C29 37D05 37C20 PDFBibTeX XMLCite \textit{V. Z. Grines}, J. Dyn. Control Syst. 6, No. 1, 97--126 (2000; Zbl 0984.37020) Full Text: DOI
Grines, V. Z. Structural stability and asymptotic behavior of invariant manifolds of \(A\)-diffeomorphisms of surfaces. (English) Zbl 0944.37009 J. Dyn. Control Syst. 3, No. 1, 91-110 (1997). MSC: 37C75 37D20 PDFBibTeX XMLCite \textit{V. Z. Grines}, J. Dyn. Control Syst. 3, No. 1, 91--110 (1997; Zbl 0944.37009) Full Text: DOI
Anosov, D. V.; Bronshtejn, I. U.; Aranson, S. Kh.; Grines, V. Z. Smooth dynamical systems. (English. Russian original) Zbl 0658.58002 Dynamical systems I, Encycl. Math. Sci. 1, 149-233 (1988); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 1, 151-242 (1985). MSC: 58-02 37C10 37C75 54H20 PDFBibTeX XML
Aranson, S. Kh.; Grines, V. Z. Topological classification of flows on closed two-dimensional manifolds. (English. Russian original) Zbl 0615.58015 Russ. Math. Surv. 41, No. 1, 183-208 (1986); translation from Usp. Mat. Nauk 41, No. 1, 149-169 (1986). Reviewer: C.Pastur MSC: 37C10 34C05 34D30 PDFBibTeX XMLCite \textit{S. Kh. Aranson} and \textit{V. Z. Grines}, Russ. Math. Surv. 41, No. 1, 183--208 (1986; Zbl 0615.58015); translation from Usp. Mat. Nauk 41, No. 1, 149--169 (1986) Full Text: DOI
Anosov, D. V.; Bronshtejn, I. U.; Aranson, S. Kh.; Grines, V. Z. Dynamical systems. I: Smooth dynamical systems. (Russian) Zbl 0605.58001 Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 1, 151-242 (1985). Reviewer: F.Przytycki MSC: 58-02 37Cxx 54H20 PDFBibTeX XMLCite \textit{D. V. Anosov} et al., Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 1, 151--242 (1985; Zbl 0605.58001)