Regular and Chaotic Dynamics最新文献_第2页

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>We consider a skew product (F_{A}=(sigma_{omega},A)) over irrational rotation (sigma_{omega}(x)=x+omega) of a circle (mathbb{T}^{1}). It is supposed that the transformation (A:mathbb{T}^{1}to SL(2,mathbb{R}))\u0000which is a (C^{1})-map has the form (A(x)=Rbig{(}varphi(x)big{)}Zbig{(}lambda(x)big{)}), where (R(varphi)) is a rotation in (mathbb{R}^{2}) through the angle (varphi) and (Z(lambda)=text{diag}{lambda,lambda^{-1}}) is a diagonal matrix. Assuming that (lambda(x)geqslantlambda_{0}>1) with a sufficiently large constant (lambda_{0}) and the function (varphi)\u0000is such that (cosvarphi(x)) possesses only simple zeroes, we study hyperbolic properties of\u0000the cocycle generated by (F_{A}). We apply the critical set method to show that, under some\u0000additional requirements on the derivative of the function (varphi), the secondary collisions compensate weakening of the hyperbolicity due to primary collisions and the cocycle generated by (F_{A}) becomes uniformly hyperbolic\u0000in contrast to the case where secondary collisions can be partially eliminated.</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

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, Borislav Gajić, Božidar Jovanović","doi":"10.1134/S1560354723010057","DOIUrl":"10.1134/S1560354723010057","url":null,"abstract":"<div>We consider the nonholonomic systems of (n) homogeneous balls (mathbf{B}_{1},dots,mathbf{B}_{n}) with the same radius (r) that are rolling without slipping about a fixed sphere (mathbf{S}_{0}) with center (O) and radius (R).\u0000In addition, it is assumed that a dynamically nonsymmetric sphere (mathbf{S}) with the center that coincides with the center (O) of the fixed sphere (mathbf{S}_{0}) rolls without\u0000slipping in contact with the moving balls (mathbf{B}_{1},dots,mathbf{B}_{n}). 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 (n=1) 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 (n) homogeneous balls of the same radius, but with different\u0000masses, which roll without slipping\u0000over a fixed plane (Sigma_{0}) with a plane (Sigma) that moves without slipping over these balls.</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

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

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

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

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

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

引用次数: 0

Synchronization and Bistability of Two Uniaxial Spin-Transfer Oscillators with Field Coupling 具有场耦合的两个单轴自旋转移振荡器的同步和双稳性

IF 1.4 4区数学

Regular and Chaotic Dynamics Pub Date : 2022-12-10 DOI: 10.1134/S1560354722060077

Pavel V. Kuptsov

{"title":"Synchronization and Bistability of Two Uniaxial Spin-Transfer Oscillators with Field Coupling","authors":"Pavel V. Kuptsov","doi":"10.1134/S1560354722060077","DOIUrl":"10.1134/S1560354722060077","url":null,"abstract":"<div>A spin-transfer oscillator is a nanoscale device demonstrating self-sustained\u0000precession of its magnetization vector whose length is preserved. Thus, the\u0000phase space of this dynamical system is limited by a three-dimensional\u0000sphere. A generic oscillator is described by the Landau – Lifshitz – Gilbert – Slonczewski\u0000equation, and we consider a particular case of uniaxial symmetry when the\u0000equation yet experimentally relevant is reduced to a dramatically simple\u0000form. The established regime of a single oscillator is a purely sinusoidal limit\u0000cycle coinciding with a circle of sphere latitude (assuming that points where\u0000the symmetry axis passes through the sphere are the poles). On the limit cycle\u0000the governing equations become linear in two oscillating magnetization vector components\u0000orthogonal to the axis, while the third one along the axis remains constant. In this paper\u0000we analyze how this effective linearity manifests itself when two such oscillators are\u0000mutually coupled via their magnetic fields. Using the phase approximation approach, we\u0000reveal that the system can exhibit bistability between\u0000synchronized and nonsynchronized oscillations. For the synchronized one the Adler equation is derived, and the\u0000estimates for the boundaries of the bistability area are obtained. The two-dimensional\u0000slices of the basins of attraction of the two coexisting solutions are\u0000considered. They are found to be embedded in each other, forming a series of\u0000parallel stripes. Charts of regimes and charts of Lyapunov exponents are computed\u0000numerically. Due to the effective linearity the overall structure of the\u0000charts is very simple; no higher-order synchronization tongues except the main\u0000one are observed.</div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"27 6","pages":"697 - 712"},"PeriodicalIF":1.4,"publicationDate":"2022-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4415626","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