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Regular and Chaotic Dynamics最新文献

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Construction of an Anosov Spatial Linkage Anosov空间联动的构造
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-02-27 DOI: 10.1134/S1560354726510040
Shu Sakaguchi, Mitsuru Shibayama
{"title":"Construction of an Anosov Spatial Linkage","authors":"Shu Sakaguchi,&nbsp;Mitsuru Shibayama","doi":"10.1134/S1560354726510040","DOIUrl":"10.1134/S1560354726510040","url":null,"abstract":"<div><p>The triple linkage of Thurston and Weeks exhibits Anosov behavior for certain parameter values,\u0000which can be shown by examining the Gauss curvature of the configuration space equipped with the metric induced by kinetic energy.\u0000In this paper, we consider a spatial linkage that can be viewed as a conversion of the triple linkage.\u0000We show that the configuration space asymptotically becomes a Riemannian submanifold of the four-dimensional torus <span>(mathbb{T}^{4})</span> taking the limit of the parameters.\u0000Through verified numerical computation, we demonstrate that the asymptotic configuration space has negative curvature,\u0000and hence that for parameters close to the limit the linkage is Anosov by structural stability of an Anosov flow.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 4","pages":"518 - 530"},"PeriodicalIF":0.8,"publicationDate":"2026-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614383","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
On the Singularities in the Dynamics of a Spherical Top with Nonholonomic Constraints 非完整约束球面顶动力学中的奇异性
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-02-27 DOI: 10.1134/S1560354726510015
Alexander P. Ivanov, Georgy M. Maurakh
{"title":"On the Singularities in the Dynamics of a Spherical Top with Nonholonomic Constraints","authors":"Alexander P. Ivanov,&nbsp;Georgy M. Maurakh","doi":"10.1134/S1560354726510015","DOIUrl":"10.1134/S1560354726510015","url":null,"abstract":"<div><p>The problem of the motion of a dynamically symmetric ball with a shifted center of gravity on a horizontal absolutely rough plane is considered, taking into account the unilateral nature of the contact. It is shown that for some values of the parameters and initial conditions, singularities of two types may appear: ambiguity in determining the subsequent motion (separation of the body from the support or continuation of rolling) or the impossibility of determining it within the framework of the model used (the finite time paradox). For a formal description of these situations, the generalized complementarity problem is used. The Littlewood problem of the rolling of a hoop with a point mass is studied in detail. Some cases of paradoxes when imposing differential constraints of various types are also discussed, including the generalization of the Chaplygin sleigh and the “rubber” ball.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 Editors:","pages":"336 - 347"},"PeriodicalIF":0.8,"publicationDate":"2026-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147637005","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
Nondeterministic Billiards 不确定的台球
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-02-27 DOI: 10.1134/S1560354726510039
Manuel Quaschner
{"title":"Nondeterministic Billiards","authors":"Manuel Quaschner","doi":"10.1134/S1560354726510039","DOIUrl":"10.1134/S1560354726510039","url":null,"abstract":"<div><p>We consider a new type of billiard trajectories of point-particles moving freely in <span>(d)</span>-dimensional space until collision. At collisions of two or more particles we have scattering at a subspace with a co-dimension of at least <span>(d)</span> preserving only the total momentum of the colliding particles, but the internal direction and kinetic energy can change arbitrary and even an exchange of mass is possible. Hence the future of the trajectory is nondeterministic. Motivated by questions concerning non-collision singularities in the <span>(n)</span>-body problem, for which these systems might serve as approximations, we are mainly interested in the asymptotic growth rate for trajectories that have infinitely many collisions and are expanding. For this case we provide as our main results exponential lower bounds for the diameter and the kinetic energy of the system in the number of so-called chain-closing collisions.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 4","pages":"591 - 631"},"PeriodicalIF":0.8,"publicationDate":"2026-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614425","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
On the Finiteness Issue of Four-Body Balanced Configurations in the Plane 平面上四体平衡构型的有限性问题
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-02-27 DOI: 10.1134/S1560354726510052
Yuchen Wang, Lei Zhao
{"title":"On the Finiteness Issue of Four-Body Balanced Configurations in the Plane","authors":"Yuchen Wang,&nbsp;Lei Zhao","doi":"10.1134/S1560354726510052","DOIUrl":"10.1134/S1560354726510052","url":null,"abstract":"<div><p>For any given positive masses, we prove that the number of <span>(mathbf{S})</span>-balanced configurations of four bodies in the plane is finite up to similitudes, provided that the symmetric matrix <span>(mathbf{S})</span> is sufficiently close to a numerical matrix. To establish this result, we utilize singular sequences to analyze the possible degenerate algebraic varieties defined by <span>(mathbf{S})</span>-balanced configurations. We derive all potential singular diagrams, encompassing both equal-order and non-equal-order cases. In the equal-order case, we obtain the necessary mass equations, while for <span>(mathbf{S})</span> approaching the identity matrix, we demonstrate the absence of non-equal-order singular sequences, thereby rigorously rule out all non-generic scenarios. Furthermore, we extend this conclusion to the five-body scenario.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 4","pages":"560 - 590"},"PeriodicalIF":0.8,"publicationDate":"2026-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614424","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: The Lagrange Identity and Dynamics in a Potential Jacobi Field 位雅可比场的拉格朗日恒等式和动力学
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-02-12 DOI: 10.1134/S1560354726010041
Valery V. Kozlov
{"title":"Erratum to: The Lagrange Identity and Dynamics in a Potential Jacobi Field","authors":"Valery V. Kozlov","doi":"10.1134/S1560354726010041","DOIUrl":"10.1134/S1560354726010041","url":null,"abstract":"","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 Editors:","pages":"175 - 175"},"PeriodicalIF":0.8,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S1560354726010041.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147338475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Complex Algebraic Caustics in Planar and Projective Billiards 平面和射影台球中的复代数焦散
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-02-12 DOI: 10.1134/S1560354726010016
Alexey A. Glutsyuk
{"title":"On Complex Algebraic Caustics in Planar and Projective Billiards","authors":"Alexey A. Glutsyuk","doi":"10.1134/S1560354726010016","DOIUrl":"10.1134/S1560354726010016","url":null,"abstract":"<div><p>A <i>caustic</i> of a billiard is a curve whose tangent lines are reflected to its own tangent lines. A billiard is called <i>Birkhoff caustic-integrable</i> if there exists a topological annulus adjacent to its boundary from inside that is foliated by\u0000closed caustics. The famous Birkhoff Conjecture, studied by many mathematicians, states that <i>the only Birkhoff caustic-integrable billiards are ellipses.</i> The conjecture is open even for billiards whose boundaries are ovals of algebraic curves. In this case the billiard is known to have a dense family of so-called rational caustics that are also ovals of algebraic curves.\u0000We introduce the notion of a\u0000<i>complex caustic:</i> a complex algebraic curve whose <i>complex</i> tangent lines are sent by complexified reflection to its own\u0000complex tangent lines.\u0000We show that the usual billiard on a real planar curve <span>(gamma)</span> has a complex caustic if and only if <span>(gamma)</span> is a conic. We prove an analogous result for billiards on all the surfaces of constant curvature. These results are corollaries of the solution of S. Bolotin’s polynomial integrability conjecture: a joint result by M. Bialy, A. Mironov and the author. We extend them\u0000to the projective billiards introduced by S. Tabachnikov, which are a common generalization of billiards on surfaces of constant curvature. We also deal with a well-known class of projective billiards on conics that are defined to have caustics forming a dual conical pencil. We show that, up to restriction to a finite union of arcs, each of them is equivalent to a billiard on an appropriate surface of constant curvature.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 Editors:","pages":"132 - 149"},"PeriodicalIF":0.8,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147338840","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 Perturbations of the Spectrum ofa One-Dimensional (mathcal{PT})-Symmetric Periodic Schrödinger Operator 对一维(mathcal{PT}) -对称周期Schrödinger算子谱的扰动的勘误
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-02-12 DOI: 10.1134/S156035472601003X
Petr G. Grinevich, Iskander A. Taimanov
{"title":"Erratum to: On Perturbations of the Spectrum of\u0000a One-Dimensional (mathcal{PT})-Symmetric Periodic Schrödinger Operator","authors":"Petr G. Grinevich,&nbsp;Iskander A. Taimanov","doi":"10.1134/S156035472601003X","DOIUrl":"10.1134/S156035472601003X","url":null,"abstract":"","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 Editors:","pages":"174 - 174"},"PeriodicalIF":0.8,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S156035472601003X.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147338902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Erratum to: On the Problem of Stability of Viscous Shocks 关于粘性冲击稳定性问题的勘误
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-02-12 DOI: 10.1134/S1560354726010028
Sergey V. Bolotin, Dmitry V. Treschev
{"title":"Erratum to: On the Problem of Stability of Viscous Shocks","authors":"Sergey V. Bolotin,&nbsp;Dmitry V. Treschev","doi":"10.1134/S1560354726010028","DOIUrl":"10.1134/S1560354726010028","url":null,"abstract":"","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 Editors:","pages":"173 - 173"},"PeriodicalIF":0.8,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S1560354726010028.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147338479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rhomboidal Central Configurations of the Five-Body Problem 五体问题的菱形中心构型
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-12-30 DOI: 10.1134/S1560354725560011
Ke-Ming Chang, Kuo-Chang Chen
{"title":"Rhomboidal Central Configurations of the Five-Body Problem","authors":"Ke-Ming Chang,&nbsp;Kuo-Chang Chen","doi":"10.1134/S1560354725560011","DOIUrl":"10.1134/S1560354725560011","url":null,"abstract":"<div><p>In this paper we investigate rhomboidal central configurations for the planar five-body problem.\u0000These are configurations whose convex hulls are rhombuses, and one interior mass lies on a diagonal of the rhombus.\u0000Consider partition of the configuration space by orderings of mutual distances,\u0000our main theorem provides criteria for central configurations in every region of this partition.\u0000For some regions we obtain existence and uniqueness of central configurations, for some we obtain\u0000nonexistence, for others our criteria are necessary conditions on masses.\u0000Our proofs are elementary and completely analytic.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 3","pages":"468 - 483"},"PeriodicalIF":0.8,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148061282","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
Traveling Wave Solutions of the Burgers – Gardner Equation with a Nonlinear Source 非线性源下Burgers - Gardner方程的行波解
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-12-30 DOI: 10.1134/S1560354725560047
Nikolay A. Kudryashov
{"title":"Traveling Wave Solutions of the Burgers – Gardner Equation with a Nonlinear Source","authors":"Nikolay A. Kudryashov","doi":"10.1134/S1560354725560047","DOIUrl":"10.1134/S1560354725560047","url":null,"abstract":"<div><p>The Burgers – Gardner equation with a nonlinear source is considered. The Cauchy problem for this equation cannot be solved by the inverse scattering transform and we look for the traveling wave solutions. The Painlevé test is used to find constraints on the parameters of the equation for its integrability. The first integral of the nonlinear ordinary differential equation is obtained taking into account the results of the\u0000Painlevé test. The first integral thus found is used to obtain the general solution\u0000of the equation. Some exact solutions are found by means of the simplest equation method.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 Editors:","pages":"83 - 91"},"PeriodicalIF":0.8,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342875","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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