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A Characterization of Multiplicity-Preserving Global Bifurcations of Complex Polynomial Vector Fields
Springer Science and Business Media LLC - Tập 19 Số 3 - 2020
Kealey Dias
Maximal invariant sets for restrictions of tent and unimodal maps
Springer Science and Business Media LLC - Tập 2 - Trang 385-398 - 2001
Carlos Gustavo Tamm de Araujo Moreira
The aim of this paper is to study the restriction of a tent mapf: I → I to a subintervalJ ∋ I, and to characterize when the maximal invariant off⋎J is a countable set. We shall extend our results for a certain class of unimodal maps, via a semi-conjugacy. In the case of tent maps there is a critical case where the maximal invariant set is a Cantor set with Hausdorff dimension zero. The caracteriza...... hiện toàn bộ
Asymptotic Stability of Coupled Oscillators with Time-Dependent Damping
Springer Science and Business Media LLC - Tập 15 - Trang 553-573 - 2015
Jitsuro Sugie
The present paper is devoted to an investigation on the asymptotic stability for the damped oscillators with multiple degrees of freedom, $$\begin{aligned} {\mathbf {x}}'' + h(t)\,{\mathbf {x}}' + A\,{\mathbf {x}} = {\mathbf {0}} \end{aligned}$$ a...... hiện toàn bộ
KAM Tori for a Two Dimensional Beam Equation with a Quintic Nonlinear Term and Quasi-periodic Forcing
Springer Science and Business Media LLC - Tập 21 - Trang 1-43 - 2022
Min Zhang, Jie Rui, Yan Li, Jian Zhang
This work studies a two-dimensional beam equation with a quintic nonlinear term and quasi-periodic forcing $$\begin{aligned} u_{tt}+\Delta ^2 u+ \varepsilon \phi (t)h(u)=0,\quad x\in {\mathbb {T}}^2,\quad t\in {\mathbb {R}} \end{aligned}$$ with periodic boundary conditions, where ...... hiện toàn bộ
On the Solutions of Ordinary Differential Equations in the Form of Dulac Series
Springer Science and Business Media LLC - Tập 21 - Trang 1-16 - 2022
V. S. Samovol
We consider a nonlinear ordinary differential equation of arbitrary order with coefficients in the form of power series that converge in a neighborhood of the origin. The methods created in power geometry in recent years make it possible to compute formal solutions to that equation in the form of Dulac series. We describe the corresponding algorithm and prove a sufficient convergence condition for...... hiện toàn bộ
Nonholonomic systems and the geometry of constraints
Springer Science and Business Media LLC - Tập 5 - Trang 247-259 - 2004
Marcelo H. Kobayashi, Waldyr M. Oliva
In a recent paper [9] we analyze conservation of volume for a series of examples of mechanical systems with linear, affine and non linear constraints aiming to make evident some geometric aspects related with them. Here, we only consider examples with linear constraints (defined by a constant rank distribution), in which we have conservation of volume. Conservation of volume means, equivalently, t...... hiện toàn bộ
Inverse Scattering Transform and Dynamics of Soliton Solutions for Nonlocal Focusing Modified Korteweg-de Vries Equation
Springer Science and Business Media LLC - - 2024
Xiao-Fan Zhang, Shou-Fu Tian, Jin-Jie Yang, Tian-Tian Zhang
The Riemann–Hilbert problem is developed to study the general N-soliton solution of the nonlocal modified Korteweg-de Vries equation in this work. The key to proving this result is the analysis of the Riemann–Hilbert problem related to the Cauchy problem of the nonlocal modified Korteweg-de Vries equation. The general N-soliton solution is acquired by solving the Riemann–Hilbert problem of the non...... hiện toàn bộ
Dynamical Behavior of a Stochastic Microorganism Flocculation Model with Nonlinear Perturbation
Springer Science and Business Media LLC - Tập 21 - Trang 1-19 - 2022
Xiaojie Mu, Daqing Jiang, Ahmed Alsaedi
Due to many uncertain factors, the microorganism flocculation models could be affected by environmental noise. The paper aims to discuss the dynamical behavior of a stochastic microorganism flocculation model, including the extinction and the persistence. Moreover, the expression of density function near the positive equilibrium point is explicitly obtained. Our results indicate that a larger whit...... hiện toàn bộ
Dynamics of One-Dimensional Motion of a Gas Under the Influence of Monochromatic Radiation
Springer Science and Business Media LLC - Tập 22 - Trang 1-21 - 2023
Dig Vijay Tanwar, P. K. Sahu
The concern with the dispersion of shock waves in perfect gas in the context of monochromatic radiation is mentioned in this manuscript. The system of Hyperbolic nonlinear partial differential equations (NLPDEs) is used to address this issue. In order to study aforementioned equations, invariance under Lie symmetry analysis is performed. Therefore, commutative relations, symmetry groups and adjoin...... hiện toàn bộ
Classification of permutations and cycles of maximum topological entropy
Springer Science and Business Media LLC - Tập 4 - Trang 77-97 - 2003
Deborah M. King, John B. Strantzen
Iff is a continuous self-map of a compact interval we can represent each finite fully invariant set off by a permutation. We can then calculate the topological entropy of the permutation. This provides us with a numerical measure of complexity for any map which exhibits a given permutation type. In this paper we present cyclic and noncyclic permutations which have maximum topological entropy among...... hiện toàn bộ
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