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Remizov, Alexey Olegovich

Total publications: 34 (32)
in MathSciNet: 28 (28)
in zbMATH: 28 (28)
in Web of Science: 21 (21)
in Scopus: 29 (29)
Cited articles: 20
Citations in Math-Net.Ru: 62
Citations in Web of Science: 61
Citations in Scopus: 112
Presentations: 8

Number of views:
This page:7761
Abstract pages:8475
Full texts:1376
References:709
Remizov, Alexey Olegovich
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: http://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:
  1. A.O. Remizov, “Geodesics on 2-surfaces with pseudo-Riemannian metric: singularities of changes of signature”, Sb. Math., 200:3 (2009), 385–403  crossref  mathscinet  zmath
  2. I.R. Shafarevich, A.O. Remizov, Linear Algebra and Geometry, Springer-Verlag Berlin and Heidelberg GmbH, 2013 (English)  crossref  mathscinet  zmath
  3. 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  crossref  mathscinet  zmath
  4. A.O. Remizov, “On the local and global properties of geodesics in pseudo-Riemannian metrics”, Differential Geometry and its Applications, 39 (2015), 36–58  crossref  mathscinet  zmath
  5. A.O. Remizov, F. Tari, “Singularities of the geodesic flow on surfaces with pseudo-Riemannian metrics”, Geometriae Dedicata, 185:1 (2016), 131–153  crossref  mathscinet  zmath

http://www.mathnet.ru/eng/person12248
List of publications on Google Scholar
http://zbmath.org/authors/?q=ai:remizov.alexey-o
https://mathscinet.ams.org/mathscinet/MRAuthorID/645213
http://elibrary.ru/author_items.asp?spin=1661-5786
http://orcid.org/0000-0003-0405-2417
http://www.researcherid.com/rid/S-2108-2016
http://www.scopus.com/authid/detail.url?authorId=7005553945
https://www.researchgate.net/profile/Alexey_Remizov

Full list of publications:
| by years | by types | by times cited in WoS | by times cited in Scopus | scientific publications | common list |



   2019
1. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus

   2018
2. A. O. Remizov, “On isomorphisms of pseudo-Euclid spaces”, Math. Ed., 2018, no. 2(86), 15–39  mathnet  elib
3. 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  crossref  mathscinet  zmath  isi  scopus (cited: 1)
4. 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  crossref  mathscinet  zmath  isi  scopus
5. 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  crossref  mathscinet  zmath  scopus (cited: 1)
6. 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  crossref  mathscinet  zmath

   2017
7. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 1)  elib  scopus (cited: 1)
8. N. G. Pavlova, A. O. Remizov, “Smooth functions, formal series, Whitney theorems, finished”, Math. Ed., 2017, no. 3(83), 13–27  mathnet  elib

   2016
9. A. O. Remizov, “Geodesics in generalized Finsler spaces: singularities in dimension two”, J. Singularities, 14:1 (2016), 172–193  crossref  mathscinet  zmath
10. A. O. Remizov, F. Tari, “Singularities of the geodesic flow on surfaces with pseudo-Riemannian metrics”, Geometriae Dedicata, 185:1 (2016), 131–153  crossref  mathscinet  zmath  isi (cited: 4)  scopus (cited: 5)
11. N. G. Pavlova, A. O. Remizov, “Smooth Functions, Formal Series, and Whitney Theorems”, Math. Ed., 2016, no. 3(79), 49–65  mathnet  elib

   2015
12. A. O. Remizov, “On the local and global properties of geodesics in pseudo-Riemannian metrics”, Differ. Geom. Appl., 39 (2015), 36–58  crossref  mathscinet  zmath  isi (cited: 3)  scopus (cited: 4)
13. 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  crossref  isi (cited: 4)  elib  scopus (cited: 5)

   2014
14. I. R. Shafarevich, A. O. Remizov, Linear Algebra and Geometry, 2nd edition, IKI Edition, Izhevsk, 2014 , 554 pp. "Mathesis"
15. 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  crossref  mathscinet  zmath  isi (cited: 22)  scopus (cited: 23)
16. 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  crossref  mathscinet  zmath  isi  scopus

   2013
17. 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"  crossref  mathscinet  zmath  scopus (cited: 34)

   2012
18. 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  crossref  mathscinet  zmath  isi (cited: 4)  scopus (cited: 5)

   2011
19. N. G. Pavlova, A. O. Remizov, “Geodesics on hypersurfaces in Minkowski space: singularities of signature change”, Russian Math. Surveys, 66:6 (2011), 1201–1203  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 3)  elib  elib  scopus (cited: 4)  scopus (cited: 4)

   2010
20. A. O. Remizov, “On geodesics in metrics with singularities of the Klein type”, Russian Math. Surveys, 65:1 (2010), 180–182  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 3)  elib  elib  scopus (cited: 3)
21. A. O. Remizov, “Singularities of a geodesic flow on surfaces with a cuspidal edge”, Proc. Steklov Inst. Math., 268 (2010), 248–257  mathnet  crossref  mathscinet  zmath  isi (cited: 4)  elib  scopus (cited: 4)

   2009
22. A. O. Remizov, “Geodesics on 2-surfaces with pseudo-Riemannian metric: singularities of changes of signature”, Sb. Math., 200:3 (2009), 385–403  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 6)  elib  elib  scopus (cited: 5)
23. I. R. Shafarevich, A. O. Remizov, Linear Algebra and Geometry, 1st edition, eds. A. S. Kuleshov, Fizmatlit, Moscow, 2009 , 511 pp. "Fizmatlit"  mathscinet  zmath

   2008
24. A. O. Remizov, “Codimension-two singularities in 3D affine control systems with a scalar control”, Sb. Math., 199:4 (2008), 613–627  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  elib  scopus (cited: 2)
25. 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  mathnet  crossref  mathscinet  zmath  isi (cited: 2)  elib  elib  scopus (cited: 1)

   2007
26. A. O. Remizov, “Singularities in three-dimensional affine control systems with scalar control”, Russian Math. Surveys, 62:4 (2007), 821–822  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus

   2008
27. A. O. Remizov, “Multidimensional Poincare Construction and Singularities of Lifted Fields For Implicit Differential Equations”, Journal of Mathematical Sciences, 151:6 (2008), 3561–3602  mathnet  crossref  mathscinet  zmath  scopus (cited: 11)

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

   2002
29. 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  mathnet  crossref  mathscinet  zmath  isi  scopus
30. A. O. Remizov, “On Proper Singular Points of Ordinary Differential Equations Unsolved for Derivatives”, Differ. Equ., 38:5 (2002), 654–662  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1)
31. A. O. Remizov, “Implicit differential equations and vector fields with non-isolated singular points”, Sb. Math., 193:11 (2002), 1671–1690  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  elib  scopus (cited: 1)
32. A. O. Remizov, “Generic singular points of implicit differential equations”, Mosc. Univ. Math. Bull., 57:5 (2002), 9–15  mathnet  mathscinet  zmath  scopus (cited: 1)
33. A. O. Remizov, “Vector fields with nonisolated singular points”, Dokl. Math., 65:3 (2002), 437–439  mathnet  mathscinet  zmath  isi  scopus

   2001
34. 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  mathscinet  zmath  scopus

Presentations in Math-Net.Ru
1. 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
2. Особенности геодезических потоков в двумерных метриках переменной сигнатуры
A. O. Remizov
Geometric theory of optimal control
March 13, 2019 16:45
3. Особенности геодезических потоков в двумерных метриках переменной сигнатуры
A. O. Remizov

December 24, 2018 16:45
4. Гипоэллиптическая диффузия и ее применение для восстановления изображений
A. O. Remizov
Geometric theory of optimal control
October 25, 2017 18:30
5. Особенности геодезических потоков в двумерных метриках переменной сигнатуры (продолжение)
A. O. Remizov
Dynamical systems and differential equations
October 16, 2017 18:30
6. Особенности геодезических потоков в двумерных метриках переменной сигнатуры
A. O. Remizov
Dynamical systems and differential equations
November 21, 2016 18:30
7. 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
8. Особенности и ренормальные формы поднятых векторных полей
A. O. Remizov
Seminar of the Department of Differential Equations, Steklov Mathematical Institute of RAS
December 21, 2005

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