{"results":[{"id":"doaj_10.46298/ocnmp.12890","title":"Simple conditions for the transformation of dynamical coordinates into canonical ones in Hamiltonian dynamics","authors":[{"name":"Patrick Cassam-Chenaï"}],"abstract":"We obtain conditions, which when fulfilled, permit to transform the coordinates of a dynamical system into pairs of canonical ones for some Hamiltonian system. These conditions, restricted to the class of coordinate transformations which act on each coordinate independently, are greatly simplified. However, they are surprisingly successful in defining canonical coordinates and an associated Hamiltonian for several test examples. So, a method is proposed to exploit these simple transformations in a systematic manner.","source":"DOAJ","year":2024,"language":"","subjects":["Mathematics"],"doi":"10.46298/ocnmp.12890","url":"http://ocnmp.episciences.org/12890/pdf","pdf_url":"http://ocnmp.episciences.org/12890/pdf","is_open_access":true,"published_at":"","score":68},{"id":"ss_7ee120b02ff59c19d15314bd06810f6c8c7497de","title":"The cubic Darboux systems with a non-elementary singular point at the Poincar\\'{e} equator","authors":[{"name":"E. Volokitin"}],"abstract":"We study the global behavior of the trajectories of the polynomial system $\\dot x = x - x^2 y+p x y^2+ y^3, \\ \\dot y=y+p y^3 , \\ \\ p\\in \\mathbb{R}$. Our study is related to the paper {\\it Alarcon B., Castro S.B.S.D., Labouriau I.S.} Glodal planar dynamics with star nodes: beyond Hilbert's 16th problem//arXiv:2106/07516v2 [math.DS].","source":"Semantic Scholar","year":2023,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/7ee120b02ff59c19d15314bd06810f6c8c7497de","is_open_access":true,"published_at":"","score":67},{"id":"doaj_10.46298/ocnmp.8631","title":"ON THE PROPAGATION OF EQUATORIAL WAVES INTERACTING WITH A NON-UNIFORM CURRENT","authors":[{"name":"Emil Novruzov"}],"abstract":"We consider the propagation of equatorial waves of small amplitude, in a flow with an underlying non-uniform current. Without making the too restrictive rigid-lid approximation, by exploiting the available Hamiltonian structure of the problem, we derive the dispersion relation for the propagation of coupled long-waves: a surface wave and an internal wave. Also, we investigate the above-mentioned model of wave-current interactions in the general case with arbitrary vorticities.","source":"DOAJ","year":2022,"language":"","subjects":["Mathematics"],"doi":"10.46298/ocnmp.8631","url":"https://ocnmp.episciences.org/8631/pdf","pdf_url":"https://ocnmp.episciences.org/8631/pdf","is_open_access":true,"published_at":"","score":66},{"id":"ss_be8ce27c6d2e98dc836edaa68007c71dfdf6d17d","title":"Amenable upper mean dimensions","authors":[{"name":"Zhiming Li"}],"abstract":"","source":"Semantic Scholar","year":2021,"language":"en","subjects":["Mathematics"],"doi":"10.1007/s13324-021-00538-9","url":"https://www.semanticscholar.org/paper/be8ce27c6d2e98dc836edaa68007c71dfdf6d17d","is_open_access":true,"citations":5,"published_at":"","score":65.15},{"id":"crossref_10.1134/s1995080221120337","title":"DS Normal Distribution: Properties and Applications","authors":[{"name":"P. Sulewski"}],"abstract":"","source":"CrossRef","year":2021,"language":"en","subjects":null,"doi":"10.1134/s1995080221120337","url":"https://doi.org/10.1134/s1995080221120337","pdf_url":"https://link.springer.com/content/pdf/10.1134/S1995080221120337.pdf","is_open_access":true,"citations":3,"published_at":"","score":65.09},{"id":"ss_562c9a899bd6103ff635c61295554794a6cb724c","title":"Sandpiles on the Square Lattice","authors":[{"name":"Robert D. Hough"},{"name":"D. Jerison"},{"name":"Lionel Levine"}],"abstract":"AbstractWe give a non-trivial upper bound for the critical density when stabilizing i.i.d. distributed sandpiles on the lattice $${\\mathbb{Z}^2}$$Z2 . We also determine the asymptotic spectral gap, asymptotic mixing time, and prove a cutoff phenomenon for the recurrent state abelian sandpile model on the torus $${\\left(\\mathbb{Z}/m\\mathbb{Z}\\right)^2}$$Z/mZ2 . The techniques use analysis of the space of functions on $${\\mathbb{Z}^2}$$Z2 which are harmonic modulo 1. In the course of our arguments, we characterize the harmonic modulo 1 functions in $${\\ell^p(\\mathbb{Z}^2)}$$ℓp(Z2) as linear combinations of certain discrete derivatives of Green’s functions, extending a result of Schmidt and Verbitskiy (Commun Math Phys 292(3):721–759, 2009. arXiv:0901.3124 [math.DS]).","source":"Semantic Scholar","year":2017,"language":"en","subjects":["Physics","Mathematics"],"doi":"10.1007/s00220-019-03408-5","url":"https://www.semanticscholar.org/paper/562c9a899bd6103ff635c61295554794a6cb724c","is_open_access":true,"citations":19,"published_at":"","score":61.57},{"id":"ss_6b980b107434f78c0c1d3414be1e6e0c50790af0","title":"KAM Theory for secondary tori","authors":[{"name":"L. Biasco"},{"name":"L. Chierchia"}],"abstract":"In [3] (Rend. Lincei Mat. Appl. 26 (2015), 1-10; see also arXiv:1503.08145 [math.DS]) the following result has been announced: Theorem. Consider a real-analytic nearly-integrable mechanical system with potential $f$, namely, a Hamiltonian system with real-analytic Hamiltonian $$H(y,x)=\\frac12 \\sum_{i=1}^n y_i^2 +\\epsilon f(x)\\ ,$$ $(y,x)\\in{\\mathbb R}^n\\times{\\mathbb T}^n$ being standard action--angle variables. For \"general non-degenerate\" potentials $f$'s there exists $\\epsilon_0,a\u003e0$ such that, if $0\u003c\\epsilon\u003c\\epsilon_0$, then the Liouville measure of the complementary of $H$-invariant tori is smaller than $\\epsilon|\\log \\epsilon|^a$. In this paper we provide a proof of such result.","source":"Semantic Scholar","year":2017,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/6b980b107434f78c0c1d3414be1e6e0c50790af0","is_open_access":true,"citations":7,"published_at":"","score":61.21},{"id":"ss_0b1c54dcbc69c6c06f7edc0df917351060235e66","title":"The structure theory of Nilspaces II: Representation as nilmanifolds","authors":[{"name":"Yonatan Gutman"},{"name":"Freddie Manners"},{"name":"P. P. Varj'u"}],"abstract":"This paper forms the second part of a series of three papers by the authors concerning the structure of nilspaces of Antolín Camarena and Szegedy. A nilspace is a compact space X X together with closed collections of cubes C n ( X ) ⊆ X 2 n C_n(X)\\subseteq X^{2^n} , n = 1 , 2 , … n=1,2,\\ldots satisfying some natural axioms. From these axioms it follows that a nilspace can be built as a finite tower of extensions where each of the successive fibers is a compact abelian group. Our main result is a new proof of a result due to Antolín Camarena and Szegedy [Nilspaces, nilmanifolds and their morphisms, arXiv:1009.3825v3 (2012)] stating that if each of these groups is a torus, then X X is isomorphic (in a strong sense) to a nilmanifold G / Γ G/\\Gamma . We also extend the theorem to a setting where the nilspace arises from a dynamical system ( X , T ) (X,T) . These theorems are a key stepping stone towards the general structure theorem in [The structure theory of nilspaces III: Inverse limit representations and topological dynamics, arXiv:1605.08950v1 [math.DS] (2016)] (which again closely resembles the main theorem of Antolín Camarena and Szegedy). The main technical tool, enabling us to deduce algebraic information from topological data, consists of existence and uniqueness results for solutions of certain natural functional equations, again modelled on the theory in Antolín Camarena and Szegedy’s paper.","source":"Semantic Scholar","year":2016,"language":"en","subjects":["Mathematics"],"doi":"10.1090/TRAN/7503","url":"https://www.semanticscholar.org/paper/0b1c54dcbc69c6c06f7edc0df917351060235e66","pdf_url":"https://doi.org/10.1090/tran/7503","is_open_access":true,"citations":27,"published_at":"","score":60.81},{"id":"ss_e90bb6ba2092f8a828fbfff5361ebe810ace9d05","title":"Fatou Components of Attracting Skew-Products","authors":[{"name":"Han Peters"},{"name":"I. M. Smit"}],"abstract":"We investigate the existence of wandering Fatou components for polynomial skew-products in two complex variables. In 2004, the non-existence of wandering domains near a super-attracting invariant fiber was shown in Lilov (Fatou theory in two dimensions, PhD thesis, University of Michigan, 2004). In 2014, it was shown in Astorg et al. (Ann Math, arXiv:1411.1188 [math.DS], 2014) that wandering domains can exist near a parabolic invariant fiber. In Peters and Vivas (Math Z, arXiv:1408.0498, 2014), the geometrically attracting case was studied, and we continue this study here. We prove the non-existence of wandering domains for subhyperbolic attracting skew-products; this class contains the maps studied in Peters and Vivas (Math Z, arXiv:1408.0498, 2014). Using expansion properties on the Julia set in the invariant fiber, we prove bounds on the rate of escape of critical orbits in almost all fibers. Our main tool in describing these critical orbits is a possibly singular linearization map of unstable manifolds.","source":"Semantic Scholar","year":2015,"language":"en","subjects":["Mathematics","Medicine"],"doi":"10.1007/s12220-017-9811-6","url":"https://www.semanticscholar.org/paper/e90bb6ba2092f8a828fbfff5361ebe810ace9d05","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs12220-017-9811-6.pdf","is_open_access":true,"citations":25,"published_at":"","score":59.75},{"id":"crossref_10.1007/s10958-015-2604-1","title":"Characteristic Functionals of Probabilistic Measures in DS-Groups and Related Topics","authors":[{"name":"V. Tarieladze"}],"abstract":"","source":"CrossRef","year":2015,"language":"en","subjects":null,"doi":"10.1007/s10958-015-2604-1","url":"https://doi.org/10.1007/s10958-015-2604-1","pdf_url":"http://link.springer.com/content/pdf/10.1007/s10958-015-2604-1.pdf","is_open_access":true,"citations":1,"published_at":"","score":59.03},{"id":"ss_f4eae90f3e36a49b6ec459eb4777c2e50470757e","title":"Existence of attractors for three-dimensional flows","authors":[{"name":"C. Morales"}],"abstract":"We prove the results in [1] using Theorem 1 of the recent paper [2] by Crovisier and Yang. References: [1] Arbieto, A., Rojas, C., Santiago, B., Existence of attractors, homoclinic tangencies and singular-hyperbolicity for flows, arXiv:1308.1734v1 [math.DS] 8 Aug 2013. [2] Crovisier, S., Yang, D., On the density of singular hyperbolic three-dimensional vector fields: a conjecture of Palis, arXiv:1404.5130v1 [math.DS] 21 Apr 2014.","source":"Semantic Scholar","year":2014,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/f4eae90f3e36a49b6ec459eb4777c2e50470757e","is_open_access":true,"citations":1,"published_at":"","score":58.03},{"id":"ss_cb433e472f4c568497463eadd6edc0706e8dea06","title":"Ergodic Properties of $k$-Free Integers in Number Fields","authors":[{"name":"F. Cellarosi"},{"name":"I. Vinogradov"}],"abstract":"Let $K/\\mathbf Q$ be a degree $d$ extension. Inside the ring of integers $\\mathcal O_K$ we define the set of $k$-free integers $\\mathcal F_k$ and a natural $\\mathcal O_K$-action on the space of binary $\\mathcal O_K$-indexed sequences, equipped with an $\\mathcal O_K$-invariant probability measure associated to $\\mathcal F_k$. We prove that this action is ergodic, has pure point spectrum and is isomorphic to a $\\mathbf Z^d$-action on a compact abelian group. In particular, it is not weakly mixing and has zero measure-theoretical entropy. This work generalizes the paper by the first author and Sinai arXiv:1112.4691 [math.DS] where $K=\\mathbf Q$ and $k=2$.","source":"Semantic Scholar","year":2013,"language":"en","subjects":["Mathematics"],"doi":"10.3934/JMD.2013.7.461","url":"https://www.semanticscholar.org/paper/cb433e472f4c568497463eadd6edc0706e8dea06","pdf_url":"http://arxiv.org/pdf/1304.0214.pdf","is_open_access":true,"citations":34,"published_at":"","score":58.02},{"id":"ss_f2fde38eb5d77b4d8dcb100ff90c4940d037e545","title":"Stable Configurations of repelling Points on compact Manifolds","authors":[{"name":"Burton Randol"}],"abstract":"This is an expanded version of [arXiv:1107.4836v1 [math.DS]]. Using techniques from [Chapter XI, The Selberg Trace Formula, in Eigenvalues in Riemannian Geometry, by Isaac Chavel], in which a differential-geometrically intrinsic treatment of counterparts of classical electrostatics was introduced, it is shown that on some compact manifolds, certain stable configurations of points which mutually repel along all interconnecting geodesics become equidistributed as the number of points increases.","source":"Semantic Scholar","year":2012,"language":"en","subjects":["Physics","Mathematics"],"doi":"10.1090/S0002-9939-2014-12007-7","url":"https://www.semanticscholar.org/paper/f2fde38eb5d77b4d8dcb100ff90c4940d037e545","pdf_url":"https://www.ams.org/proc/2014-142-08/S0002-9939-2014-12007-7/S0002-9939-2014-12007-7.pdf","is_open_access":true,"citations":1,"published_at":"","score":56.03},{"id":"ss_22226afb51ded7fae304a5fd199d7571ede3cfa1","title":"Non-integrability of open billiard flows and Dolgopyat-type estimates","authors":[{"name":"L. Stoyanov"}],"abstract":"","source":"Semantic Scholar","year":2011,"language":"en","subjects":["Mathematics"],"doi":"10.1017/S0143385710000933","url":"https://www.semanticscholar.org/paper/22226afb51ded7fae304a5fd199d7571ede3cfa1","is_open_access":true,"citations":24,"published_at":"","score":55.72},{"id":"doaj_10.46298/dmtcs.2971","title":"Product decomposition for surjective 2-block NCCA","authors":[{"name":"Felipe García-Ramos"}],"abstract":"In this paper we define products of one-dimensional Number Conserving Cellular Automata (NCCA) and show that surjective NCCA with 2 blocks (i.e radius 1/2) can always be represented as products of shifts and identites. In particular, this shows that surjective 2-block NCCA are injective.","source":"DOAJ","year":2011,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.2971","url":"https://dmtcs.episciences.org/2971/pdf","pdf_url":"https://dmtcs.episciences.org/2971/pdf","is_open_access":true,"published_at":"","score":55},{"id":"doaj_10.46298/dmtcs.2977","title":"The structure of communication problems in cellular automata","authors":[{"name":"Raimundo Briceño"},{"name":"Pierre-Etienne Meunier"}],"abstract":"Studying cellular automata with methods from communication complexity appears to be a promising approach. In the past, interesting connections between communication complexity and intrinsic universality in cellular automata were shown. One of the last extensions of this theory was its generalization to various \"communication problems'', or \"questions'' one might ask about the dynamics of cellular automata. In this article, we aim at structuring these problems, and find what makes them interesting for the study of intrinsic universality and quasi-orders induced by simulation relations.","source":"DOAJ","year":2011,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.2977","url":"https://dmtcs.episciences.org/2977/pdf","pdf_url":"https://dmtcs.episciences.org/2977/pdf","is_open_access":true,"published_at":"","score":55},{"id":"doaj_10.46298/dmtcs.2978","title":"A fixed point theorem for Boolean networks expressed in terms of forbidden subnetworks","authors":[{"name":"Adrien Richard"}],"abstract":"We are interested in fixed points in Boolean networks, $\\textit{i.e.}$ functions $f$ from $\\{0,1\\}^n$ to itself. We define the subnetworks of $f$ as the restrictions of $f$ to the hypercubes contained in $\\{0,1\\}^n$, and we exhibit a class $\\mathcal{F}$ of Boolean networks, called even or odd self-dual networks, satisfying the following property: if a network $f$ has no subnetwork in $\\mathcal{F}$, then it has a unique fixed point. We then discuss this \"forbidden subnetworks theorem''. We show that it generalizes the following fixed point theorem of Shih and Dong: if, for every $x$ in $\\{0,1\\}^n$, there is no directed cycle in the directed graph whose the adjacency matrix is the discrete Jacobian matrix of $f$ evaluated at point $x$, then $f$ has a unique fixed point. We also show that $\\mathcal{F}$ contains the class $\\mathcal{F'}$ of networks whose the interaction graph is a directed cycle, but that the absence of subnetwork in $\\mathcal{F'}$ does not imply the existence and the uniqueness of a fixed point.","source":"DOAJ","year":2011,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.2978","url":"https://dmtcs.episciences.org/2978/pdf","pdf_url":"https://dmtcs.episciences.org/2978/pdf","is_open_access":true,"published_at":"","score":55},{"id":"doaj_10.46298/dmtcs.2972","title":"Orbits of the Bernoulli measure in single-transition asynchronous cellular automata","authors":[{"name":"Henryk Fukś"},{"name":"Andrew Skelton"}],"abstract":"We study iterations of the Bernoulli measure under nearest-neighbour asynchronous binary cellular automata (CA) with a single transition. For these CA, we show that a coarse-level description of the orbit of the Bernoulli measure can be obtained, that is, one can explicitly compute measures of short cylinder sets after arbitrary number of iterations of the CA. In particular, we give expressions for probabilities of ones for all three minimal single-transition rules, as well as expressions for probabilities of blocks of length 3 for some of them. These expressions can be interpreted as \"response curves'', that is, curves describing the dependence of the final density of ones on the initial density of ones.","source":"DOAJ","year":2011,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.2972","url":"https://dmtcs.episciences.org/2972/pdf","pdf_url":"https://dmtcs.episciences.org/2972/pdf","is_open_access":true,"published_at":"","score":55},{"id":"doaj_10.46298/dmtcs.2969","title":"Projective subdynamics and universal shifts","authors":[{"name":"Pierre Guillon"}],"abstract":"We study the projective subdynamics of two-dimensional shifts of finite type, which is the set of one-dimensional configurations that appear as columns in them. We prove that a large class of one-dimensional shifts can be obtained as such, namely the effective subshifts which contain positive-entropy sofic subshifts. The proof involves some simple notions of simulation that may be of interest for other constructions. As an example, it allows us to prove the undecidability of all non-trivial properties of projective subdynamics.","source":"DOAJ","year":2011,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.2969","url":"https://dmtcs.episciences.org/2969/pdf","pdf_url":"https://dmtcs.episciences.org/2969/pdf","is_open_access":true,"published_at":"","score":55},{"id":"ss_c0cf16ceacfa14af6d142ae205bb19138634d1c4","title":"Topology Proceedings 52 (2018) pp. 321-328: A Suspension Flow over the Full Shift with Two Distinct Measures of Maximal Entropy","authors":[{"name":"D. Thompson"},{"name":"T. Kucherenko"},{"name":"D. Thompson"}],"abstract":"","source":"Semantic Scholar","year":2008,"language":"en","subjects":null,"url":"https://www.semanticscholar.org/paper/c0cf16ceacfa14af6d142ae205bb19138634d1c4","is_open_access":true,"citations":2,"published_at":"","score":52.06}],"total":1096819,"page":1,"page_size":20,"sources":["CrossRef","DOAJ","Semantic Scholar"],"query":"math.DS"}