Persons: Remizov, Alexey Olegovich

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Remizov, Alexey Olegovich

Total publications:	42 (38)
in MathSciNet:	32 (32)
in zbMATH:	32 (32)
in Web of Science:	24 (24)
in Scopus:	29 (29)
Cited articles:	26
Citations:	260
Presentations:	14

Number of views:
This page:	14179
Abstract pages:	15735
Full texts:	4983
References:	1311

Candidate of physico-mathematical sciences (2003)

Speciality:

01.01.02 (Differential equations, dynamical systems, and optimal control)

Birth date:

11.11.1973

E-mail:

Website:

https://www.researchgate.net/profile/Alexey_Remizov

Keywords:

ordinary differential equations, singular points, resonance, normal form, blowing-up, invariant manifold, geodesic flow, pseudo-Riemannian metric, degeneracy

Subject:

singularities in the theory of ordinary differential equations, dynamical systems, differential geometry, calculus of variations, and optimal control. Recently, the main theme of the work is singularities of geodesic flows in pseudo-Riemannian spaces with signature varying metrics. In particular, it was established that geodesic lines cannot pass through degenerate points of the metric in arbitrary tangential directions, but only in certain admissible directions. Generically, in 2-dimensional case, the number of admissible directions is finite and varies from one to three, but if the dimension is more than two, the number of admissible directions can be finite or infinite. A brief survey in the two-dimensional case is presented in: https://arxiv.org/pdf/1801.09815.pdf

Main publications:

A.O. Remizov, “Geodesics on 2-surfaces with pseudo-Riemannian metric: singularities of changes of signature”, Sb. Math., 200:3 (2009), 385–403
I.R. Shafarevich, A.O. Remizov, Linear Algebra and Geometry, Springer-Verlag Berlin and Heidelberg GmbH, 2013 (English)
R. Ghezzi, A.O. Remizov, “On a class of vector fields with discontinuities of divide-by-zero type and its applications to geodesics in singular metrics”, J. Dyn. Control Syst., 18:1 (2012), 135–158
A.O. Remizov, “On the local and global properties of geodesics in pseudo-Riemannian metrics”, Differential Geometry and its Applications, 39 (2015), 36–58
A.O. Remizov, F. Tari, “Singularities of the geodesic flow on surfaces with pseudo-Riemannian metrics”, Geometriae Dedicata, 185:1 (2016), 131–153

https://www.mathnet.ru/eng/person12248

List of publications on Google Scholar

https://zbmath.org/authors/ai:remizov.alexey-o

https://mathscinet.ams.org/mathscinet/MRAuthorID/645213

https://elibrary.ru/author_items.asp?spin=1661-5786

https://orcid.org/0000-0003-0405-2417

https://publons.com/researcher/2178636

https://www.webofscience.com/wos/author/record/S-2108-2016

https://www.scopus.com/authid/detail.url?authorId=7005553945

https://www.researchgate.net/profile/Alexey_Remizov

https://arxiv.org/a/remizov_a_1

Full list of publications:

scientific publications

by years

by types

by times cited

common list

		Citations (Crossref Cited-By Service + Math-Net.Ru)


2023
1.	A. O. Remizov, “Singularities of quasi-linear differential equations”, Dal'nevost. Mat. Zh., 23:1 (2023), 85–105
2.	A. O. Remizov, “Los caprichos diferenciales. A series of plots about differential equations”, Math. Ed., 2023, no. 1(105), 32–47
3.	A. O. Remizov, “To the centenary of I.R. Shafarevich”, Math. Ed., 2023, no. 4(108), 2–9

2022
4.	N. G. Pavlova, A. O. Remizov, Introduction to Singularity Theory, MIPT, Moscow, 2022 , 181 pp. "Researchgate"

2021
5.	N. G. Pavlova, A. O. Remizov, “Hyperbolic Roussarie fields with degenerate quadratic part”, Russian Math. Surveys, 76:2 (2021), 366–368
6.	N. G. Pavlova, A. O. Remizov, “Smooth Local Normal Forms of Hyperbolic Roussarie Vector Fields”, Moscow Math. Journal, 21:2 (2021), 413–426	2 ^[x]

2020
7.	N. G. Pavlova, A. O. Remizov, “Correction to the article “Smooth functions, formal series and Whitney theorems ””, Math. Ed., 2020, no. 1(93), 69

2019
8.	N. G. Pavlova, A. O. Remizov, “Completion of the classification of generic singularities of geodesic flows in two classes of metrics”, Izv. Math., 83:1 (2019), 104–123

2018
9.	A. O. Remizov, “On isomorphisms of pseudo-Euclid spaces”, Math. Ed., 2018, no. 2(86), 15–39
10.	U. Boscain, R. A. Chertovskih, J. P. Gauthier, D. Prandi, A. O. Remizov, “Highly Corrupted Image Inpainting Through Hypoelliptic Diffusion”, J. Math. Imaging Vis., 60:8 (2018), 1231–1245	17 ^[x]
11.	N. G. Pavlova, A. O. Remizov, “On isomorphisms of pseudo-Euclidean spaces with signature (p,n-p) for p = 2,3”, Linear Algebra Appl., 541 (2018), 60–80
12.	N. G. Pavlova, A. O. Remizov, “A brief survey on singularities of geodesic flows in smooth signature changing metrics on 2-surfaces”, Advances in Singularities and Foliations: Geometry, Topology and Applications (Salvador, Brazil, 2015), Springer Proc. in Math. & Stat., 222, Springer, 2018, 135–155	2 ^[x]
13.	U. Boscain, R. A. Chertovskih, J. P. Gauthier, D. Prandi, A. O. Remizov, “Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion”, ESAIM, Proc. Surv., 64 (2018), 37–53	5 ^[x]

2017
14.	N. G. Pavlova, A. O. Remizov, “A complete classification of generic singularities of geodesic flows on 2-surfaces with pseudo-Riemannian metrics”, Russian Math. Surveys, 72:3 (2017), 577–579
15.	N. G. Pavlova, A. O. Remizov, “Smooth functions, formal series, Whitney theorems, finished”, Math. Ed., 2017, no. 3(83), 13–27

2016
16.	A. O. Remizov, “Geodesics in generalized Finsler spaces: singularities in dimension two”, J. Singularities, 14:1 (2016), 172–193	2 ^[x]
17.	A. O. Remizov, F. Tari, “Singularities of the geodesic flow on surfaces with pseudo-Riemannian metrics”, Geometriae Dedicata, 185:1 (2016), 131–153	8 ^[x]
18.	N. G. Pavlova, A. O. Remizov, “Smooth Functions, Formal Series, and Whitney Theorems”, Math. Ed., 2016, no. 3(79), 49–65

2015
19.	A. O. Remizov, “On the local and global properties of geodesics in pseudo-Riemannian metrics”, Differ. Geom. Appl., 39 (2015), 36–58	7 ^[x]
20.	U. Boscain, J. P. Gauthier, D. Prandi, A. O. Remizov, “Image Reconstruction Via Non-Isotropic Diffusion in Dubins/Reed-Shepp-like Control Systems”, 53-rd IEEE Conference on Decision and Control (Los Angeles, USA, 15-17 Dec. 2014), Proceedings of the IEEE Conference on Decision and Control, 2015, 4278–4283	10 ^[x]

2014
21.	I. R. Shafarevich, A. O. Remizov, Linear Algebra and Geometry, 2nd edition, IKI Edition, Izhevsk, 2014 , 554 pp. "Mathesis"
22.	U. Boscain, R. A. Chertovskih, J. P. Gauthier, A. O. Remizov, “Hypoelliptic diffusion and human vision: a semidiscrete new twist”, SIAM J. Imaging Sci., 7:2 (2014), 669–698	39 ^[x]
23.	R. A. Chertovskih, A. O. Remizov, “On pleated singular points of first-order implicit differential equations”, J. Dyn. Control Syst., 20:2 (2014), 197–206

2013
24.	I. R. Shafarevich, A. O. Remizov, Linear Algebra and Geometry, Springer, Heidelberg, 2013 , xxii+526 pp., Translated from the 2009 Russian original by David Kramer and Lena Nekludova, "Springer"	60 ^[x]

2012
25.	R. Ghezzi, A. O. Remizov, “On a class of vector fields with discontinuities of divide-by-zero type and its applications to geodesics in singular metrics”, J. Dyn. Control Syst., 18:1 (2012), 135–158	8 ^[x]

2011
26.	N. G. Pavlova, A. O. Remizov, “Geodesics on hypersurfaces in Minkowski space: singularities of signature change”, Russian Math. Surveys, 66:6 (2011), 1201–1203

2010
27.	A. O. Remizov, “On geodesics in metrics with singularities of the Klein type”, Russian Math. Surveys, 65:1 (2010), 180–182
28.	A. O. Remizov, “Singularities of a geodesic flow on surfaces with a cuspidal edge”, Proc. Steklov Inst. Math., 268 (2010), 248–257

2009
29.	A. O. Remizov, “Geodesics on 2-surfaces with pseudo-Riemannian metric: singularities of changes of signature”, Sb. Math., 200:3 (2009), 385–403
30.	I. R. Shafarevich, A. O. Remizov, Linear Algebra and Geometry, 1st edition, eds. A. S. Kuleshov, Fizmatlit, Moscow, 2009 , 511 pp. "Fizmatlit"

2008
31.	A. O. Remizov, “Codimension-two singularities in 3D affine control systems with a scalar control”, Sb. Math., 199:4 (2008), 613–627
32.	V. M. Zakalyukin, A. O. Remizov, “Legendre Singularities in Systems of Implicit ODEs and Slow–Fast Dynamical Systems”, Proc. Steklov Inst. Math., 261 (2008), 136–148

2007
33.	A. O. Remizov, “Singularities in three-dimensional affine control systems with scalar control”, Russian Math. Surveys, 62:4 (2007), 821–822

2008
34.	A. O. Remizov, “Multidimensional Poincare Construction and Singularities of Lifted Fields For Implicit Differential Equations”, Journal of Mathematical Sciences, 151:6 (2008), 3561–3602

2005
35.	A. O. Remizov, “On vector fields generated by implicit differential equations”, J. Math. Sci., 126:6 (2005), 1643–1653

2002
36.	A. O. Remizov, “Improper Singular Points of Corank 1 of Systems of Differential Equations Not Solved for the Derivatives”, Differ. Equ., 38:8 (2002), 1122–1131
37.	A. O. Remizov, “On Proper Singular Points of Ordinary Differential Equations Unsolved for Derivatives”, Differ. Equ., 38:5 (2002), 654–662
38.	A. O. Remizov, “Implicit differential equations and vector fields with non-isolated singular points”, Sb. Math., 193:11 (2002), 1671–1690
39.	A. O. Remizov, “Generic singular points of implicit differential equations”, Mosc. Univ. Math. Bull., 57:5 (2002), 9–15
40.	A. O. Remizov, “Vector fields with nonisolated singular points”, Dokl. Math., 65:3 (2002), 437–439
41.	A. O. Remizov, “On typical singularities of implicit differential equations”, Progress in nonlinear science (Nizhny Novgorod, 2001), 1, RAS, Inst. Appl. Phys., 2002, 346–352	5 ^[x]

2001
42.	A. O. Remizov, “Error estimate for an approximate solution of an ODE system which is not solved with respect to the derivatives”, Mosc. Univ. Comput. Math. Cybern., 2001, no. 2, 30–37

Presentations in Math-Net.Ru

1.	Singularities of geodesic flows in $2D$ metrics with varying signature A. O. Remizov Noncommutative geometry and topology April 4, 2024 16:45
2.	Восстановление изображений математическими методами A. O. Remizov Mathematical seminar Faculty of Computer Science HSE February 3, 2023 18:10
3.	Дифференциальные уравнения F(x,y,y')=0 с точки зрения геометрии и особенностей A. O. Remizov April 21, 2022 18:30
4.	Hyperbolic Rousarie vector fields A. O. Remizov Mathematical Physics, Dynamical Systems and Infinite-Dimensional Analysis – 2021 July 5, 2021 13:00
5.	Singularities of geodesic flows in 2D signature varying metrics A. O. Remizov Optimization and nonlinear analysis April 15, 2021 14:00
6.	Особенности геодезических потоков в 2D метриках переменной сигнатуры: десять лет спустя A. O. Remizov Differential geometry and applications October 5, 2020 17:45
7.	Восстановление изображений методами субримановой геометрии A. O. Remizov Mathematical Workshop of the School of Applied Mathematics and Computer Science (MIPT) April 12, 2019 18:30
8.	Особенности геодезических потоков в двумерных метриках переменной сигнатуры A. O. Remizov Geometric Theory of Optimal Control March 13, 2019 16:45
9.	Особенности геодезических потоков в двумерных метриках переменной сигнатуры A. O. Remizov Hamiltonian systems and statistical mechanics December 24, 2018 16:45
10.	Гипоэллиптическая диффузия и ее применение для восстановления изображений A. O. Remizov Geometric Theory of Optimal Control October 25, 2017 18:30
11.	Особенности геодезических потоков в двумерных метриках переменной сигнатуры (продолжение) A. O. Remizov Dynamical systems and differential equations October 16, 2017 18:30
12.	Особенности геодезических потоков в двумерных метриках переменной сигнатуры A. O. Remizov Dynamical systems and differential equations November 21, 2016 18:30
13.	Singularities of geodesic flows for singular metrics (pseudo-Riemannian and of the Klein type) A. O. Remizov Differential geometry and applications April 18, 2011 16:45
14.	Особенности и ренормальные формы поднятых векторных полей A. O. Remizov Seminar "Optimal Control and Dynamical Systems" December 21, 2005

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