# zbMATH — the first resource for mathematics

## Parasyuk, Igor O.

Compute Distance To:
 Author ID: parasyuk.igor-o Published as: Parasyuk, I.; Parasyuk, I. O.; Parasyuk, Igor; Parasyuk, Igor O. External Links: MGP · Wikidata · ORCID
 Documents Indexed: 75 Publications since 1973, including 1 Book
all top 5

#### Co-Authors

 32 single-authored 10 Samoĭlenko, Anatoliĭ Mykhaĭlovych 4 Perestyuk, Mykola Oleksiĭovych 4 Zakharin, Sergei F. 3 Lovejkin, Yu. V. 3 Lukovsky, Ivan Oleksandrovych 3 Makarov, Volodymyr Leonidovich 3 Pozur, Sergij V. 3 Sharkovskiĭ, Oleksandr Mykolaiovych 2 Antonishin, I. O. 2 Berezans’kyĭ, Yuriĭ Makarovych 2 Boĭchuk, Oleksandr Andriĭovych 2 Denysenko, Oleksandr M. 2 Fushchych, Vil’gel’m Illich 2 Korolyuk, Volodymyr Semenovych 2 Kubichka, Andrij A. 2 Lahoda, V. A. 2 Nikitin, A. H. 2 Protsak, L. V. 2 Repeta, B. V. 2 Rustamova, Anna 2 Stanzhyts’ky, O. M. 2 Tkachenko, Victor Ivanovich 2 Vakal, Yu. E. 1 Antonyuk, Oleksandra Viktorivna 1 Diblík, Josef 1 Fečkan, Michal 1 Gorodnii, M. F. 1 Horishna, Yulia 1 Hutlyans’kyi, V. Ya. 1 Kapudtyan, O. V. 1 Khruslov, Eugene Yakovlevich 1 Kiguradze, Ivan Tarielovich 1 Kirichenko, Vladimir V. 1 Kochubeĭ, Anatoliĭ Naumovych 1 Kozachenko, Yuriĭ Vasyl’ovych 1 Kulinich, Grygoriĭ L. 1 Kushnir, Roman M. 1 Lagoda, Volodymyr 1 Loveikin, Yu. V. 1 Marchenko, V. O. 1 Medveď, Milan 1 Meleshko, V’yacheslav Volodymyrovych 1 Nagornyj, Volodymyr N. 1 Pastur, Leonid Andreevich 1 Plakhotnyk, V. V. 1 Portenko, Mykola Ivanovych 1 Protsak, Lyudmyla 1 Repeta, Bogdan 1 Romanchenko, I. A. 1 Ronto, M. I. 1 Rozov, Nikolaĭ Khristovich 1 Samoĭlenko, Valeriĭ Grygorovych 1 Shevchuk, I. O. 1 Teplinsky, Yuriy V. 1 Trofimchuk, Sergei I. 1 Vyshenskij, V. A. 1 Zakhavin, S. V. 1 Zhuravlëv, Viktor Filippovich
all top 5

#### Serials

 16 Ukrainian Mathematical Journal 15 Ukraïns’kyĭ Matematychnyĭ Zhurnal 7 Visnyk. Matematyka. Mekhanika. Kyïvs’kyĭ Universytet Imeni Tarasa Shevchenka 5 Dopovidi Akademiï Nauk Ukraïns’koï RSR. Seriya A 4 Neliniĭni Kolyvannya 3 Doklady Akademii Nauk Ukrainskoĭ SSR, Seriya A 3 Journal of Mathematical Sciences (New York) 3 Electronic Journal of Differential Equations (EJDE) 3 Nonlinear Oscillations 2 Dopovidi Akademiï Nauk Ukraïni 1 Funkcialaj Ekvacioj. Serio Internacia 1 Mathematical Inequalities & Applications 1 Dopovidi Natsional’noï Akademiï Nauk Ukraïny. Matematyka, Pryrodoznavstvo, Tekhnichni Nauky 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 1 Matematychnyĭ Visnyk Naukovogo Tovarystva Im. Shevchenka
all top 5

#### Fields

 40 Ordinary differential equations (34-XX) 33 Dynamical systems and ergodic theory (37-XX) 14 Mechanics of particles and systems (70-XX) 7 Partial differential equations (35-XX) 7 Integral equations (45-XX) 4 History and biography (01-XX) 3 Differential geometry (53-XX) 2 Operator theory (47-XX) 2 Optics, electromagnetic theory (78-XX) 1 Real functions (26-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Geometry (51-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Numerical analysis (65-XX)

#### Citations contained in zbMATH

26 Publications have been cited 81 times in 64 Documents Cited by Year
Conservation of quasi-periodic motions of reversible multifrequency systems. Zbl 0502.34026
Parasyuk, I. O.
1982
Differential equations. 2nd revised ed. Zbl 1330.34005
Samoilenko, A. M.; Perestyuk, M. O.; Parasyuk, I. O.
2003
Generalized and classical almost periodic solutions of Lagrangian systems. Zbl 1141.37350
Zakharin, Sergei F.; Parasyuk, Igor O.
1999
On preservation of invariant tori of Hamiltonian systems. Zbl 0587.58019
Parasyuk, I. O.
1984
Conservation of multidimensional invariant tori of Hamiltonian systems. Zbl 0561.58017
Parasyuk, I. O.
1984
Variational approach for weak quasiperiodic solutions of quasiperiodically excited Lagrangian systems on Riemannian manifolds. Zbl 1260.37030
Parasyuk, Igor; Rustamova, Anna
2012
Bifurcation of a Whitney-smooth family of coisotropic invariant tori of a Hamiltonian system under small deformation of a symplectic structure. Zbl 0995.37047
Kubichka, A. A.; Parasyuk, I. O.
2001
On smoothness of generalized quasiperiodic solutions of Lagrangian systems on Riemannian manifolds of nonpositive curvature. Zbl 1006.37036
Zakharin, S. F.; Parasyuk, I. O.
1999
Coisotropic invariant tori of Hamiltonian systems of the quasiclassical theory of motion of a conduction electron. Zbl 0706.58062
Parasyuk, I. O.
1990
Zones of instability of the Schrödinger equation with a smooth quasiperiodic potential. Zbl 0435.34042
Parasyuk, I. O.
1978
Dynamical bifurcation of multifrequency oscillations in a fast-slow system. Zbl 1376.34045
Samoilenko, A. M.; Parasyuk, I. O.; Repeta, B. V.
2015
Integral representation of solutions to boundary-value problems on the half-line for linear ODEs with singularity of the first kind. Zbl 1172.34016
Horishna, Yulia; Parasyuk, Igor; Protsak, Lyudmyla
2008
Reduction and coisotropic invariant tori of Hamiltonian systems with non-Poisson commutative symmetries. II. Zbl 0841.58026
Parasyuk, I. O.
1994
Variables of the action-angle type on symplectic manifolds stratified by coisotropic tori. Zbl 0813.58023
Parasyuk, I. O.
1993
Hyperbolic quasiperiodic solutions of U-monotone systems on Riemannian manifolds. Zbl 1428.34063
Parasyuk, Igor O.
2019
Quasiperiodic extremals of nonautonomous Lagrangian systems on Riemannian manifolds. Zbl 1376.37109
Parasyuk, I. O.
2015
Lipschitz invariant tori of indefinite-monotone systems. Zbl 1267.37063
Samoilenko, A. M.; Parasyuk, I. O.; Lahoda, V. A.
2012
Estimate for the number of perturbed ultrasubharmonics of a system with one and a half degrees of freedom close to a Hamiltonian system. Zbl 1336.37051
Vakal, Yu. E.; Parasyuk, I. O.
2011
Existence of $$V$$-bounded solutions for non-autonomous nonlinear systems via the Ważewski topological principle. Zbl 1289.34104
Lagoda, Volodymyr; Parasyuk, Igor
2010
A theorem on perturbation of coisotropic invariant tori of locally Hamiltonian systems and its application. Zbl 1107.37050
Lovejkin, Yu. V.; Parasyuk, I. O.
2005
Substantiation of the Galerkin’s procedure for indefinite monotone quasi-periodic systems. Zbl 1034.34052
Parasyuk, I. O.; Romanchenko, I. A.
2002
Bifurcation of the Cantor set of coisotropic invariant tori of the Hamiltonian system under symplectic structure perturbation. Zbl 0935.37019
Parasyuk, I. O.
1998
Qualitative analysis of families of bounded solutions of the nonlinear three-dimensional Schrödinger equation. Zbl 0727.35127
Parasyuk, I. O.; Fushchich, V. I.
1990
Non-Poissonian commutative symmetries and multidimensional invariant tori of Hamiltonian systems. Zbl 0616.58018
Parasyuk, I. O.
1984
On the one-dimensional Schrödinger equation with almost periodic potential. Zbl 0395.35083
Parasyuk, I. O.
1978
On Galerkin’s method in the perturbation theory of invariant tori. Zbl 0358.34040
Samojlenko, A. M.; Parasyuk, I. O.
1977
Hyperbolic quasiperiodic solutions of U-monotone systems on Riemannian manifolds. Zbl 1428.34063
Parasyuk, Igor O.
2019
Dynamical bifurcation of multifrequency oscillations in a fast-slow system. Zbl 1376.34045
Samoilenko, A. M.; Parasyuk, I. O.; Repeta, B. V.
2015
Quasiperiodic extremals of nonautonomous Lagrangian systems on Riemannian manifolds. Zbl 1376.37109
Parasyuk, I. O.
2015
Variational approach for weak quasiperiodic solutions of quasiperiodically excited Lagrangian systems on Riemannian manifolds. Zbl 1260.37030
Parasyuk, Igor; Rustamova, Anna
2012
Lipschitz invariant tori of indefinite-monotone systems. Zbl 1267.37063
Samoilenko, A. M.; Parasyuk, I. O.; Lahoda, V. A.
2012
Estimate for the number of perturbed ultrasubharmonics of a system with one and a half degrees of freedom close to a Hamiltonian system. Zbl 1336.37051
Vakal, Yu. E.; Parasyuk, I. O.
2011
Existence of $$V$$-bounded solutions for non-autonomous nonlinear systems via the Ważewski topological principle. Zbl 1289.34104
Lagoda, Volodymyr; Parasyuk, Igor
2010
Integral representation of solutions to boundary-value problems on the half-line for linear ODEs with singularity of the first kind. Zbl 1172.34016
Horishna, Yulia; Parasyuk, Igor; Protsak, Lyudmyla
2008
A theorem on perturbation of coisotropic invariant tori of locally Hamiltonian systems and its application. Zbl 1107.37050
Lovejkin, Yu. V.; Parasyuk, I. O.
2005
Differential equations. 2nd revised ed. Zbl 1330.34005
Samoilenko, A. M.; Perestyuk, M. O.; Parasyuk, I. O.
2003
Substantiation of the Galerkin’s procedure for indefinite monotone quasi-periodic systems. Zbl 1034.34052
Parasyuk, I. O.; Romanchenko, I. A.
2002
Bifurcation of a Whitney-smooth family of coisotropic invariant tori of a Hamiltonian system under small deformation of a symplectic structure. Zbl 0995.37047
Kubichka, A. A.; Parasyuk, I. O.
2001
Generalized and classical almost periodic solutions of Lagrangian systems. Zbl 1141.37350
Zakharin, Sergei F.; Parasyuk, Igor O.
1999
On smoothness of generalized quasiperiodic solutions of Lagrangian systems on Riemannian manifolds of nonpositive curvature. Zbl 1006.37036
Zakharin, S. F.; Parasyuk, I. O.
1999
Bifurcation of the Cantor set of coisotropic invariant tori of the Hamiltonian system under symplectic structure perturbation. Zbl 0935.37019
Parasyuk, I. O.
1998
Reduction and coisotropic invariant tori of Hamiltonian systems with non-Poisson commutative symmetries. II. Zbl 0841.58026
Parasyuk, I. O.
1994
Variables of the action-angle type on symplectic manifolds stratified by coisotropic tori. Zbl 0813.58023
Parasyuk, I. O.
1993
Coisotropic invariant tori of Hamiltonian systems of the quasiclassical theory of motion of a conduction electron. Zbl 0706.58062
Parasyuk, I. O.
1990
Qualitative analysis of families of bounded solutions of the nonlinear three-dimensional Schrödinger equation. Zbl 0727.35127
Parasyuk, I. O.; Fushchich, V. I.
1990
On preservation of invariant tori of Hamiltonian systems. Zbl 0587.58019
Parasyuk, I. O.
1984
Conservation of multidimensional invariant tori of Hamiltonian systems. Zbl 0561.58017
Parasyuk, I. O.
1984
Non-Poissonian commutative symmetries and multidimensional invariant tori of Hamiltonian systems. Zbl 0616.58018
Parasyuk, I. O.
1984
Conservation of quasi-periodic motions of reversible multifrequency systems. Zbl 0502.34026
Parasyuk, I. O.
1982
Zones of instability of the Schrödinger equation with a smooth quasiperiodic potential. Zbl 0435.34042
Parasyuk, I. O.
1978
On the one-dimensional Schrödinger equation with almost periodic potential. Zbl 0395.35083
Parasyuk, I. O.
1978
On Galerkin’s method in the perturbation theory of invariant tori. Zbl 0358.34040
Samojlenko, A. M.; Parasyuk, I. O.
1977
all top 5

#### Cited by 61 Authors

 13 Parasyuk, Igor O. 8 Sevryuk, Mikhail Borisovich 7 Wang, Xiaocai 7 Xu, Junxiang 6 Zhang, Dongfeng 5 Li, Yong 4 Cong, Fuzhong 3 Samoĭlenko, Anatoliĭ Mykhaĭlovych 2 Burkotová, Jana 2 Cieutat, Philippe 2 Fassò, Francesco 2 Huang, Qingdao 2 Lahoda, V. A. 2 Rachůnková, Irena 2 Slyusarchuk, Vasyl Yukhimovich 2 Stanzhytskyi, Oleksandr M. 2 Weinmüller, Ewa B. 2 Yi, Yingfei 1 Bajcinca, Naim 1 Bogolyubov, Nikolaĭ Nikolaevich jun. 1 Broer, Henk W. 1 Burylko, O. A. 1 Burylko, Oleksandr 1 Feketa, Petro V. 1 Filippov, M. G. 1 Fushchych, Vil’gel’m Illich 1 Gentile, Guido 1 Giacobbe, Andrea 1 Gladilina, R. I. 1 Grigorkiv, V. S. 1 Han, Yuliang 1 Hong, Jialin 1 Huitema, G. B. 1 Karpenko, O. V. 1 Kravets, Vasyl’ I. 1 Kuang, Juhong 1 Kuzina, Yu. V. 1 Loveikin, Yu. V. 1 Martynyuk, Petro M. 1 Mazzoccoli, Alessandro 1 Mielke, Alexander 1 Misiats, Oleksandr 1 Nakonechny, O. G. 1 Prykarpatsky, Anatoliy Karolevych 1 Quispel, Gilles Reinout Willem 1 Repeta, B. V. 1 Samoĭlenko, Valeriĭ Grygorovych 1 Shen, Wenxian 1 Shevchuk, Iu. M. 1 Staněk, Svatoslav 1 Tkachenko, Victor Ivanovich 1 Vaia, Faenia 1 Vakal, Yu. E. 1 Wolfrum, Matthias 1 Yanchuk, Sergiĭ Volodymyrovych 1 Yang, Xiaomei 1 Yip, Nung Kwan 1 You, Jiangong 1 Zernov, Alexander E. 1 Zhang, Xingyong 1 Zin’ko, Petro M.
all top 5

#### Cited in 31 Serials

 14 Ukrainian Mathematical Journal 6 Journal of Mathematical Sciences (New York) 4 Journal of Mathematical Analysis and Applications 3 Journal of Differential Equations 3 Acta Applicandae Mathematicae 3 Discrete and Continuous Dynamical Systems 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Journal of Dynamics and Differential Equations 2 Chaos 2 Regular and Chaotic Dynamics 2 Qualitative Theory of Dynamical Systems 2 Nonlinear Oscillations 1 Journal of Geometry and Physics 1 Automatica 1 Journal of Soviet Mathematics 1 Transactions of the American Mathematical Society 1 Physica D 1 Applied Numerical Mathematics 1 Journal of Theoretical Probability 1 Cybernetics and Systems Analysis 1 Abstract and Applied Analysis 1 Matematychni Studiï 1 Mathematical Inequalities & Applications 1 Journal of Dynamical and Control Systems 1 Communications in Contemporary Mathematics 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 1 SIAM Journal on Applied Dynamical Systems 1 Advances in Difference Equations 1 Boundary Value Problems 1 Proceedings of the Steklov Institute of Mathematics 1 Nonlinear Analysis. Theory, Methods & Applications
all top 5

#### Cited in 17 Fields

 38 Dynamical systems and ergodic theory (37-XX) 30 Ordinary differential equations (34-XX) 19 Mechanics of particles and systems (70-XX) 5 Partial differential equations (35-XX) 5 Operator theory (47-XX) 3 Differential geometry (53-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Difference and functional equations (39-XX) 2 Probability theory and stochastic processes (60-XX) 2 Numerical analysis (65-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Real functions (26-XX) 1 Geometry (51-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX)

#### Wikidata Timeline

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.