Results 31 to 40 of about 864 (203)
The geometric lorenz attractor is a homoclinic class [PDF]
, 2004 An attractor is a transitive set to which all nearby positiveorbits converge. An example of an attractor is the geometric Lorenz attractor [GH]. In this paper we prove that the geometric Lorenz attractor is a homoclinic class.
Bautista, Serafín
openaire +2 more sources
Electronic Journal of Qualitative Theory of Differential Equations, 2021 We obtain an existence theorem of nonzero solution for a class of bounded selfadjoint operator equations. The main result contains as a special case the existence result of a nontrivial homoclinic orbit of a class of Hamiltonian systems by Coti Zelati ...
Mingliang Song, Runzhen Li
doaj +1 more source
Topics in Cognitive Science, EarlyView., 2023 Abstract Fractal fluctuations are a core concept for inquiries into human behavior and cognition from a dynamic systems perspective. Here, we present a generalized variance method for multivariate detrended fluctuation analysis (mvDFA). The advantage of this extension is that it can be applied to multivariate time series and considers intercorrelation ...
Sebastian Wallot +5 more
wiley +1 more source
Mathematics, 2022 The mean curvature problem is an important class of problems in mathematics and physics. We consider the existence of homoclinic solutions to a discrete partial mean curvature problem, which is tied to the existence of discrete solitons.
Yanshan Chen, Zhan Zhou
doaj +1 more source
Expansive homoclinic classes [PDF]
Nonlinearity, 2009 We prove that for $C^1$ generic diffeomorphisms, every expansive homoclinic class is hyperbolic.
Yang, Dawei, Gan, Shaobo
openaire +2 more sources
Homoclinic classes with shadowing [PDF]
Journal of Inequalities and Applications, 2012 Abstract We show that for C 1 generic diffeomorphisms, an isolated homoclinic class is shadow-able if and only if it is a hyperbolic basic set. Mathematics Subject Classification 2000: 37C20; 37C05; 37C29; 37D05.
Ahn, Jiweon, Lee, Keonhee, Lee, Manseob
openaire +2 more sources
Collision, explosion and collapse of homoclinic classes [PDF]
Nonlinearity, 2004 Homoclinic classes of generic $C^1$-diffeomorphisms are maximal transitive sets and pairwise disjoint. We here present a model explaining how two different homoclinic classes may intersect, failing to be disjoint. For that we construct a one-parameter family of diffeomorphisms $(g_s)_{s\in [-1,1]}$ with hyperbolic points $P$ and $Q$ having nontrivial ...
Díaz, Lorenzo J., Santoro, Bianca
openaire +2 more sources
Continuum-wise expansive homoclinic classes for robust dynamical systems
Advances in Difference Equations, 2019 In the study, we consider continuum-wise expansiveness for the homoclinic class of a kind of C1 $C^{1}$-robustly expansive dynamical system. First, we show that if the homoclinic class H(p,f) $H(p, f)$, which contains a hyperbolic periodic point p, is R ...
Manseob Lee
doaj +1 more source
Measure-expansive homoclinic classes
Osaka Journal of Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lee, Keonhee, Lee, Manseob
openaire +4 more sources
Asymptotic measure-expansiveness for generic diffeomorphisms
Open Mathematics, 2021 In this paper, we will assume MM to be a compact smooth manifold and f:M→Mf:M\to M to be a diffeomorphism. We herein demonstrate that a C1{C}^{1} generic diffeomorphism ff is Axiom A and has no cycles if ff is asymptotic measure expansive.
Lee Manseob
doaj +1 more source