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Investigation of fatigue life and active vibration control via piezoelectric elements in vehicle suspension. [PDF]

Sci Rep
Wu ZP, Wang H.
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Theta functions, broken lines and 2-marked log Gromov-Witten invariants. [PDF]

Manuscr Math
Gräfnitz T.
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On the algebraic limit cycles of quadratic systems

, 2005
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NON-ALGEBRAIC LIMIT CYCLES(Topics Around Chaotic Dynamical Systems)

NON-ALGEBRAIC LIMIT CYCLES(Topics Around Chaotic Dynamical Systems)
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Invariant Algebraic Curves and Hyperelliptic Limit Cycles of Liénard Systems

Qualitative Theory of Dynamical Systems, 2021
The paper under review studies Liénard systems of the form \[ \dot x=y, \quad \dot y=-f_m(x)y-g_n(x) \] with the focus on the following two aspects: the existence of invariant algebraic curves and hyperelliptic limit cycles of the systems. The functions \(f_m(x)\) and \(g_n(x)\) involved are real polynomials of degree \(m\) and \(n\), respectively. One
Qian, Xinjie, Shen, Yang, Yang, Jiazhong
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On the Multiplicity of Algebraic Limit Cycles

Journal of Dynamics and Differential Equations, 2012
The present paper is devoted to the problem of determining the multiplicity of the unit circle as a periodic orbit of the planar differential system \[ \dot{x}=-y+f(x, y)a(x, y), \;\dot{y}=x+f(x, y)b(x, y), \] where \(f(x, y)=x^2+y^2-1\) and \(a\), \(b\) are real polynomials of the variables \(x\) and \(y\).
García, Belén, Giné, Jaume, Grau, Maite, Pérez del Río, Jesús S.   +3 more
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On the algebraic limit cycles of Liénard systems

Nonlinearity, 2008
For the Lienard systems with fm and gn polynomials of degree m and n, respectively, we present explicit systems having algebraic limit cycles in the cases m ≥ 2 and n ≥ 2m + 1 and m ≥ 3 and n = 2m. Also we prove that the Lienard system for m = 3 and n = 5 has no hyperelliptic limit cycles.
Jaume Llibre, Xiang Zhang
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Polynomial Vector Fields with Prescribed Algebraic Limit Cycles

Geometriae Dedicata, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Planar Polynomial Systems with Non-Algebraic Limit Cycles

AIP Conference Proceedings, 2009
In this paper, we study the existence of the non‐algebraic limit cycles of the systems dxdt = Pn(x,y)+xRm(x,y) dydt = Qn(x,y)+yRm(x,y) where Pn(x,y), Qn(x,y) and Rm(x,y) are homogeneous polynomials of degrees n, n and m respectively with ...
Khalil I. T. Al-Dosary, George Maroulis, Theodore E. Simos   +2 more
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Hilbert’s 16th Problem for Algebraic Limit Cycles

2016
In this chapter we state Hilbert’s 16th problem restricted to algebraic limit cycles. Namely, consider the set Σ’ n of all real polynomial vector fields \( \chi = \left( {P,\,Q} \right)\) of degree n having real irreducible \( \left( {{\rm on}\, \mathbb{R}\left[ {x,\,y} \right]} \right)\) invariant algebraic curves.
Jaume Llibre, Rafael Ramírez
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