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Regular and Chaotic Dynamics最新文献

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Components of Stable Isotopy Connectedness of Morse – Smale Diffeomorphisms Morse - small微同态稳定同位素连通性的组成
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2022-02-04 DOI: 10.1134/S1560354722010087
Timur V. Medvedev, Elena V. Nozdrinova, Olga V. Pochinka
{"title":"Components of Stable Isotopy Connectedness of Morse – Smale Diffeomorphisms","authors":"Timur V. Medvedev,&nbsp;Elena V. Nozdrinova,&nbsp;Olga V. Pochinka","doi":"10.1134/S1560354722010087","DOIUrl":"10.1134/S1560354722010087","url":null,"abstract":"<div><p>In 1976 S. Newhouse, J. Palis and F. Takens introduced a stable arc joining two structurally stable systems on a manifold. Later in 1983 they proved that all points of a regular stable arc are structurally stable diffeomorphisms except for a finite number of bifurcation diffeomorphisms which have no cycles, no heteroclinic tangencies and which have a unique nonhyperbolic periodic orbit, this orbit being the orbit of a noncritical saddle-node or a flip which unfolds generically on the arc. There are examples of Morse – Smale diffeomorphisms on manifolds of any dimension which cannot be joined by a stable arc. There naturally arises the problem of finding an invariant defining the equivalence classes of Morse – Smale diffeomorphisms with respect to connectedness by a stable arc. In the present review we present the classification results for Morse – Smale diffeomorphisms with respect to stable isotopic connectedness and obstructions to existence of stable arcs including the authors’ recent results.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"27 1","pages":"77 - 97"},"PeriodicalIF":1.4,"publicationDate":"2022-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4159679","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 Parametric Stability of the Isosceles Triangular Libration Points in the Planar Elliptical Charged Restricted Three-body Problem 平面椭圆带电受限三体问题中等腰三角形振动点的参数稳定性
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2022-02-04 DOI: 10.1134/S1560354722010099
Yocelyn Pérez-Rothen, Lucas Rezende Valeriano, Claudio Vidal
{"title":"On the Parametric Stability of the Isosceles Triangular Libration Points in the Planar Elliptical Charged Restricted Three-body Problem","authors":"Yocelyn Pérez-Rothen,&nbsp;Lucas Rezende Valeriano,&nbsp;Claudio Vidal","doi":"10.1134/S1560354722010099","DOIUrl":"10.1134/S1560354722010099","url":null,"abstract":"<div><p>We consider the planar charged restricted elliptic three-body\u0000problem (CHRETBP). In this work\u0000we consider the parametric stability of the isosceles triangle equilibrium solution denoted by <span>(L_{4}^{iso})</span>. We construct the boundary surfaces of the stability/instability regions in the space of the parameters <span>(mu)</span>, <span>(beta)</span> and <span>(e)</span>, which are parameters of the mass, charges associated to the primaries and the eccentricity of the\u0000elliptic orbit, respectively.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"27 1","pages":"98 - 121"},"PeriodicalIF":1.4,"publicationDate":"2022-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4158466","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
ALEXEY BORISOV MEMORIAL VOLUME 阿列克谢·鲍里索夫纪念册
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2022-02-04 DOI: 10.1134/S1560354722010014
{"title":"ALEXEY BORISOV MEMORIAL VOLUME","authors":"","doi":"10.1134/S1560354722010014","DOIUrl":"10.1134/S1560354722010014","url":null,"abstract":"","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"27 1","pages":"1 - 1"},"PeriodicalIF":1.4,"publicationDate":"2022-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4158465","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 Motion of an Unbalanced Circular Disk in the Field of a Point Source 非平衡圆盘在点源场中的运动
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2022-02-04 DOI: 10.1134/S1560354722010051
Elizaveta M. Artemova, Evgeny V. Vetchanin
{"title":"The Motion of an Unbalanced Circular Disk in the Field of a Point Source","authors":"Elizaveta M. Artemova,&nbsp;Evgeny V. Vetchanin","doi":"10.1134/S1560354722010051","DOIUrl":"10.1134/S1560354722010051","url":null,"abstract":"<div><p>Describing the phenomena of the surrounding world is an interesting task that has long attracted the attention of scientists. However, even in seemingly simple phenomena, complex dynamics can be revealed. In particular, leaves on the surface of various bodies of water exhibit complex behavior.\u0000This paper addresses an idealized description of the mentioned phenomenon. Namely, the problem of the plane-parallel motion of an unbalanced circular disk moving in a stream of simple structure created by a point source (sink) is considered.\u0000Note that using point sources, it is possible to approximately simulate the work of skimmers used for cleaning swimming pools.\u0000Equations of coupled motion of the unbalanced circular disk and the point source are derived. It is shown that in the case of a fixed-position source of constant intensity the equations of motion of the disk are Hamiltonian. In addition, in the case of a balanced circular disk the equations of motion are integrable. A bifurcation analysis of the integrable case is carried out. Using a scattering map, it is shown that the equations of motion of the unbalanced disk are nonintegrable. The nonintegrability found here can explain the complex motion of leaves in surface streams of bodies of water.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"27 1","pages":"24 - 42"},"PeriodicalIF":1.4,"publicationDate":"2022-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4158470","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
The Spherical Kapitza – Whitney Pendulum 球形卡皮察-惠特尼钟摆
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2022-02-04 DOI: 10.1134/S1560354722010075
Ivan Yu. Polekhin
{"title":"The Spherical Kapitza – Whitney Pendulum","authors":"Ivan Yu. Polekhin","doi":"10.1134/S1560354722010075","DOIUrl":"10.1134/S1560354722010075","url":null,"abstract":"<div><p>In this paper we study the global dynamics of the inverted spherical pendulum with a vertically rapidly vibrating suspension point in the presence of an external horizontal periodic force field. We do not assume that this force field is weak or rapidly oscillating. Provided that the period of the vertical motion and the period of the horizontal force are commensurate, we prove that there always exists a nonfalling periodic\u0000solution, i. e., there exists an initial condition such that, along the corresponding solution, the rod of the pendulum always remains above the horizontal plane passing through the pivot point. We also show numerically that there exists an asymptotically stable nonfalling solution for a wide range of parameters of the system.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"27 1","pages":"65 - 76"},"PeriodicalIF":1.4,"publicationDate":"2022-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4159662","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 the Integrability of Circulatory Systems 关于循环系统的可积性
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2022-02-04 DOI: 10.1134/S1560354722010038
V. V. Kozlov
{"title":"On the Integrability of Circulatory Systems","authors":"V. V. Kozlov","doi":"10.1134/S1560354722010038","DOIUrl":"10.1134/S1560354722010038","url":null,"abstract":"<div><p>This paper discusses conditions for the existence of polynomial (in velocities) first integrals\u0000of the equations of motion of mechanical systems in a nonpotential force field (circulatory systems). These integrals are assumed to be single-valued smooth functions on the phase space of the system (on the space of the tangent bundle of a smooth configuration manifold). It is shown that, if the genus of the closed configuration manifold of such a system with two degrees of freedom is greater than unity, then the equations of motion admit no nonconstant single-valued polynomial integrals. Examples are given of circulatory systems with configuration space in the form of a sphere and a torus which have nontrivial polynomial laws of conservation.\u0000Some unsolved problems involved in these phenomena are discussed.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"27 1","pages":"11 - 17"},"PeriodicalIF":1.4,"publicationDate":"2022-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4159668","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: 2
A Top on a Vibrating Base: New Integrable Problem of Nonholonomic Mechanics 振动基础上的顶:非完整力学的新可积问题
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2022-02-04 DOI: 10.1134/S1560354722010026
Alexey V. Borisov, Alexander P. Ivanov
{"title":"A Top on a Vibrating Base: New Integrable Problem of Nonholonomic Mechanics","authors":"Alexey V. Borisov,&nbsp;Alexander P. Ivanov","doi":"10.1134/S1560354722010026","DOIUrl":"10.1134/S1560354722010026","url":null,"abstract":"<div><p>A spherical rigid body rolling without sliding on a horizontal support is considered. The body is axially symmetric but unbalanced (tippe top). The support performs high-frequency oscillations with small amplitude. To implement the standard averaging procedure, we present equations of motion in quasi-coordinates in Hamiltonian form with additional terms of nonholonomicity [16] and introduce a new fast time variable. The averaged system is similar to the initial one with an additional term, known as vibrational potential [8, 9, 18]. This term depends on the single variable — the nutation angle <span>(theta)</span>, and according to the work of Chaplygin [5], the averaged system is integrable. Some examples exhibit the influence of vibrations on the dynamics.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"27 1","pages":"2 - 10"},"PeriodicalIF":1.4,"publicationDate":"2022-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4160269","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: 2
Elliptic Fixed Points with an Invariant Foliation: Some Facts and More Questions 具有不变叶化的椭圆不动点:一些事实和更多问题
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2022-02-04 DOI: 10.1134/S1560354722010063
Alain Chenciner, David Sauzin, Shanzhong Sun, Qiaoling Wei
{"title":"Elliptic Fixed Points with an Invariant Foliation: Some Facts and More Questions","authors":"Alain Chenciner,&nbsp;David Sauzin,&nbsp;Shanzhong Sun,&nbsp;Qiaoling Wei","doi":"10.1134/S1560354722010063","DOIUrl":"10.1134/S1560354722010063","url":null,"abstract":"<div><p>We address the following question: let\u0000<span>(F:(mathbb{R}^{2},0)to(mathbb{R}^{2},0))</span> be an analytic local diffeomorphism defined\u0000in the neighborhood of the nonresonant elliptic fixed point 0 and\u0000let <span>(Phi)</span> be a formal conjugacy to a normal form <span>(N)</span>. Supposing\u0000<span>(F)</span> leaves invariant the foliation by circles centered at <span>(0)</span>, what is\u0000the analytic nature of <span>(Phi)</span> and <span>(N)</span>?</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"27 1","pages":"43 - 64"},"PeriodicalIF":1.4,"publicationDate":"2022-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4159678","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
Integrals of Circulatory Systems Which are Quadratic in Momenta 动量二次循环系统的积分
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2021-12-06 DOI: 10.1134/S1560354721060046
Valery V. Kozlov
{"title":"Integrals of Circulatory Systems Which are Quadratic in Momenta","authors":"Valery V. Kozlov","doi":"10.1134/S1560354721060046","DOIUrl":"10.1134/S1560354721060046","url":null,"abstract":"<div><p>This paper addresses the problem of conditions for the existence of conservation laws (first integrals) of circulatory systems which are quadratic in velocities (momenta), when the external forces are nonpotential. Under some conditions the equations of motion are reduced to Hamiltonian form with some symplectic structure and the role of the Hamiltonian is played by a quadratic integral. In some cases the equations are reduced to a conformally Hamiltonian rather than Hamiltonian form. The existence of a quadratic integral and its properties allow conclusions to be drawn on the stability of equilibrium positions of circulatory systems.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"26 6","pages":"647 - 657"},"PeriodicalIF":1.4,"publicationDate":"2021-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4244750","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: 2
Existence of a Smooth Hamiltonian Circle Action near Parabolic Orbits and Cuspidal Tori 抛物轨道和倒钩环面附近光滑哈密顿圆作用的存在性
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2021-12-06 DOI: 10.1134/S1560354721060101
Elena A. Kudryavtseva, Nikolay N. Martynchuk
{"title":"Existence of a Smooth Hamiltonian Circle Action near Parabolic Orbits and Cuspidal Tori","authors":"Elena A. Kudryavtseva,&nbsp;Nikolay N. Martynchuk","doi":"10.1134/S1560354721060101","DOIUrl":"10.1134/S1560354721060101","url":null,"abstract":"<div><p>We show that every parabolic orbit of a two-degree-of-freedom integrable system admits a <span>(C^{infty})</span>-smooth Hamiltonian\u0000circle action, which is persistent under small integrable <span>(C^{infty})</span> perturbations.\u0000We deduce from this result the structural stability of parabolic orbits and show that they are all smoothly\u0000equivalent (in the non-symplectic sense) to a standard model. As a corollary, we obtain similar results for cuspidal tori. Our proof is based on showing that\u0000every symplectomorphism of a neighbourhood of a parabolic point preserving the first integrals of motion is a Hamiltonian whose generating function is smooth and constant on the\u0000connected components of the common level sets.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"26 6","pages":"732 - 741"},"PeriodicalIF":1.4,"publicationDate":"2021-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4243961","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: 12
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