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Regular and Chaotic Dynamics最新文献

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Spiral-Like Extremals near a Singular Surface in a Rocket Control Problem 一类火箭控制问题奇异曲面附近的螺旋形极值
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-04-07 DOI: 10.1134/S1560354723020028
Mariya I. Ronzhina, Larisa A. Manita
{"title":"Spiral-Like Extremals near a Singular Surface in a Rocket Control Problem","authors":"Mariya I. Ronzhina,&nbsp;Larisa A. Manita","doi":"10.1134/S1560354723020028","DOIUrl":"10.1134/S1560354723020028","url":null,"abstract":"<div><p>In this paper, we consider the minimum time problem for a space rocket whose dynamics is given by a control-affine system with drift. The admissible control set is a disc.\u0000We study extremals in the neighbourhood of singular points of the second order.\u0000Our approach is based on applying the method of a descending system of Poisson\u0000brackets and the Zelikin – Borisov method for resolution of singularities to the Hamiltonian system of Pontryagin’s maximum principle. We show that in the neighbourhood\u0000of any singular point there is a family of spiral-like solutions of the Hamiltonian system that enter the singular point in a finite time, while the control performs an infinite number of rotations around the circle.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 2","pages":"148 - 161"},"PeriodicalIF":1.4,"publicationDate":"2023-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4282389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On (SL(2,mathbb{R}))-Cocycles over Irrational Rotations with Secondary Collisions 二次碰撞下不合理旋转上的(SL(2,mathbb{R})) -环
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-04-07 DOI: 10.1134/S1560354723020053
Alexey V. Ivanov
{"title":"On (SL(2,mathbb{R}))-Cocycles over Irrational Rotations with Secondary Collisions","authors":"Alexey V. Ivanov","doi":"10.1134/S1560354723020053","DOIUrl":"10.1134/S1560354723020053","url":null,"abstract":"<div><p>We consider a skew product <span>(F_{A}=(sigma_{omega},A))</span> over irrational rotation <span>(sigma_{omega}(x)=x+omega)</span> of a circle <span>(mathbb{T}^{1})</span>. It is supposed that the transformation <span>(A:mathbb{T}^{1}to SL(2,mathbb{R}))</span>\u0000which is a <span>(C^{1})</span>-map has the form <span>(A(x)=Rbig{(}varphi(x)big{)}Zbig{(}lambda(x)big{)})</span>, where <span>(R(varphi))</span> is a rotation in <span>(mathbb{R}^{2})</span> through the angle <span>(varphi)</span> and <span>(Z(lambda)=text{diag}{lambda,lambda^{-1}})</span> is a diagonal matrix. Assuming that <span>(lambda(x)geqslantlambda_{0}&gt;1)</span> with a sufficiently large constant <span>(lambda_{0})</span> and the function <span>(varphi)</span>\u0000is such that <span>(cosvarphi(x))</span> possesses only simple zeroes, we study hyperbolic properties of\u0000the cocycle generated by <span>(F_{A})</span>. We apply the critical set method to show that, under some\u0000additional requirements on the derivative of the function <span>(varphi)</span>, the secondary collisions compensate weakening of the hyperbolicity due to primary collisions and the cocycle generated by <span>(F_{A})</span> becomes uniformly hyperbolic\u0000in contrast to the case where secondary collisions can be partially eliminated.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 2","pages":"207 - 226"},"PeriodicalIF":1.4,"publicationDate":"2023-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4282392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Eighth International Conference GEOMETRY, DYNAMICS, INTEGRABLE SYSTEMS — GDIS 2022 Dedicated to the Memory of Alexey V. Borisov June 5–11, 2022, Zlatibor, Serbia 第八届几何，动力学，可积系统国际会议- GDIS 2022献给阿列克谢V.鲍里索夫的记忆2022年6月5-11日，兹拉蒂博尔，塞尔维亚
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-03-10 DOI: 10.1134/S156035472301001X
{"title":"The Eighth International Conference GEOMETRY, DYNAMICS, INTEGRABLE SYSTEMS — GDIS 2022 Dedicated to the Memory of Alexey V. Borisov June 5–11, 2022, Zlatibor, Serbia","authors":"","doi":"10.1134/S156035472301001X","DOIUrl":"10.1134/S156035472301001X","url":null,"abstract":"","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 1","pages":"1 - 4"},"PeriodicalIF":1.4,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4427932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spherical and Planar Ball Bearings — a Study of Integrable Cases 球面和平面球轴承——可积情况的研究
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-03-10 DOI: 10.1134/S1560354723010057
Vladimir Dragović, Borislav Gajić, Božidar Jovanović
{"title":"Spherical and Planar Ball Bearings — a Study of Integrable Cases","authors":"Vladimir Dragović,&nbsp;Borislav Gajić,&nbsp;Božidar Jovanović","doi":"10.1134/S1560354723010057","DOIUrl":"10.1134/S1560354723010057","url":null,"abstract":"<div><p>We consider the nonholonomic systems of <span>(n)</span> homogeneous balls <span>(mathbf{B}_{1},dots,mathbf{B}_{n})</span> with the same radius <span>(r)</span> that are rolling without slipping about a fixed sphere <span>(mathbf{S}_{0})</span> with center <span>(O)</span> and radius <span>(R)</span>.\u0000In addition, it is assumed that a dynamically nonsymmetric sphere <span>(mathbf{S})</span> with the center that coincides with the center <span>(O)</span> of the fixed sphere <span>(mathbf{S}_{0})</span> rolls without\u0000slipping in contact with the moving balls <span>(mathbf{B}_{1},dots,mathbf{B}_{n})</span>. The problem is considered in four different configurations, three of which are new.\u0000We derive the equations of motion and find an invariant measure for these systems.\u0000As the main result, for <span>(n=1)</span> we find two cases that are integrable by quadratures according to the Euler – Jacobi theorem.\u0000The obtained integrable nonholonomic models are natural extensions of the well-known Chaplygin ball integrable problems.\u0000Further, we explicitly integrate\u0000the planar problem consisting of <span>(n)</span> homogeneous balls of the same radius, but with different\u0000masses, which roll without slipping\u0000over a fixed plane <span>(Sigma_{0})</span> with a plane <span>(Sigma)</span> that moves without slipping over these balls.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 1","pages":"62 - 77"},"PeriodicalIF":1.4,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4428668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Roller Racer with Varying Gyrostatic Momentum: Acceleration Criterion and Strange Attractors 变陀螺静动量的滚轮赛车:加速度判据和奇异吸引子
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-03-10 DOI: 10.1134/S1560354723010070
Ivan A. Bizyaev, Ivan S. Mamaev
{"title":"Roller Racer with Varying Gyrostatic Momentum: Acceleration Criterion and Strange Attractors","authors":"Ivan A. Bizyaev,&nbsp;Ivan S. Mamaev","doi":"10.1134/S1560354723010070","DOIUrl":"10.1134/S1560354723010070","url":null,"abstract":"<div><p>In this paper we investigate a nonholonomic system with parametric excitation, a Roller Racer with variable gyrostatic momentum. We examine in detail the problem of the existence of regimes with unbounded growth of energy (nonconservative Fermi acceleration). We find a criterion for the existence of trajectories for which one of the velocity components increases withound bound and has asymptotics <span>(t^{1/3})</span>. In addition, we show that the problem under consideration reduces to analysis of a three-dimensional Poincaré map. This map exhibits both regular attractors (a fixed point, a limit cycle and a torus) and strange attractors.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 1","pages":"107 - 130"},"PeriodicalIF":1.4,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4425161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dynamics of an Unbalanced Disk with a Single Nonholonomic Constraint 具有单一非完整约束的非平衡圆盘动力学
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-03-10 DOI: 10.1134/S1560354723010069
Alexander A. Kilin, Elena N. Pivovarova
{"title":"Dynamics of an Unbalanced Disk with a Single Nonholonomic Constraint","authors":"Alexander A. Kilin,&nbsp;Elena N. Pivovarova","doi":"10.1134/S1560354723010069","DOIUrl":"10.1134/S1560354723010069","url":null,"abstract":"<div><p>The problem of the rolling of a disk on a plane is considered under the assumption that there is no slipping in the direction parallel to the horizontal diameter of the disk and that the center of mass does not move in the horizontal direction. This problem is reduced to investigating a system of three first-order differential equations. It is shown that the reduced system is reversible relative to involution of codimension one and admits a two-parameter family of fixed points. The linear stability of these fixed points is analyzed. Using numerical simulation, the nonintegrability of the problem is shown. It is proved that the reduced system admits, even in the nonintegrable case, a two-parameter family of periodic solutions. A number of dynamical effects due to the existence of involution of codimension one and to the degeneracy of the fixed points of the reduced system are found.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 1","pages":"78 - 106"},"PeriodicalIF":1.4,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4427919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Billiards Within Ellipsoids in the (4)-Dimensional Pseudo-Euclidean Spaces (4)维伪欧几里德空间中椭球体内的台球
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-03-10 DOI: 10.1134/S1560354723010033
Vladimir Dragović, Milena Radnović
{"title":"Billiards Within Ellipsoids in the (4)-Dimensional Pseudo-Euclidean Spaces","authors":"Vladimir Dragović,&nbsp;Milena Radnović","doi":"10.1134/S1560354723010033","DOIUrl":"10.1134/S1560354723010033","url":null,"abstract":"<div><p>We study billiard systems within an ellipsoid in the <span>(4)</span>-dimensional pseudo-Euclidean spaces. We provide an analysis and description of periodic and weak periodic trajectories in algebro-geometric and functional-polynomial terms.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 1","pages":"14 - 43"},"PeriodicalIF":1.4,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4429601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Integrable Systems Associated to the Filtrations of Lie Algebras 与李代数滤波相关的可积系统
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-03-10 DOI: 10.1134/S1560354723010045
Božidar Jovanović, Tijana Šukilović, Srdjan Vukmirović
{"title":"Integrable Systems Associated to the Filtrations of Lie Algebras","authors":"Božidar Jovanović,&nbsp;Tijana Šukilović,&nbsp;Srdjan Vukmirović","doi":"10.1134/S1560354723010045","DOIUrl":"10.1134/S1560354723010045","url":null,"abstract":"<div><p>In 1983 Bogoyavlenski conjectured that, if the Euler equations on a Lie algebra <span>(mathfrak{g}_{0})</span> are integrable, then their certain extensions to semisimple lie algebras <span>(mathfrak{g})</span> related to the filtrations of Lie algebras\u0000<span>(mathfrak{g}_{0}subsetmathfrak{g}_{1}subsetmathfrak{g}_{2}dotssubsetmathfrak{g}_{n-1}subsetmathfrak{g}_{n}=mathfrak{g})</span> are integrable as well.\u0000In particular, by taking <span>(mathfrak{g}_{0}={0})</span> and natural filtrations of <span>({mathfrak{so}}(n))</span> and <span>(mathfrak{u}(n))</span>, we have\u0000Gel’fand – Cetlin integrable systems. We prove the conjecture\u0000for filtrations of compact Lie algebras <span>(mathfrak{g})</span>: the system is integrable in a noncommutative sense by means of polynomial integrals.\u0000Various constructions of complete commutative polynomial integrals for the system are also given.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 1","pages":"44 - 61"},"PeriodicalIF":1.4,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4430305","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quasiperiodic Version of Gordon’s Theorem 戈登定理的拟周期版本
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-03-10 DOI: 10.1134/S1560354723010021
Sergey V. Bolotin, Dmitry V. Treschev
{"title":"Quasiperiodic Version of Gordon’s Theorem","authors":"Sergey V. Bolotin,&nbsp;Dmitry V. Treschev","doi":"10.1134/S1560354723010021","DOIUrl":"10.1134/S1560354723010021","url":null,"abstract":"<div><p>We consider Hamiltonian systems possessing families of nonresonant invariant tori whose frequencies are all collinear.\u0000Then under certain conditions the frequencies depend on energy only.\u0000This is a generalization of the well-known Gordon’s theorem about periodic solutions of Hamiltonian systems.\u0000While the proof of Gordon’s theorem uses Hamilton’s principle, our result is based on Percival’s variational principle. This work was motivated by the problem of isochronicity in Hamiltonian systems.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 1","pages":"5 - 13"},"PeriodicalIF":1.4,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4734317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Erratum to: On Some Invariants of Birkhoff Billiards Under Conjugacy 关于共轭条件下Birkhoff台球的一些不变量的勘误
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2022-12-10 DOI: 10.1134/S1560354722060107
Comlan E. Koudjinan, Vadim Kaloshin
{"title":"Erratum to: On Some Invariants of Birkhoff Billiards Under Conjugacy","authors":"Comlan E. Koudjinan,&nbsp;Vadim Kaloshin","doi":"10.1134/S1560354722060107","DOIUrl":"10.1134/S1560354722060107","url":null,"abstract":"","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"27 6","pages":"757 - 757"},"PeriodicalIF":1.4,"publicationDate":"2022-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4416001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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