102 citations · 287 across the 18 of their papers we have counts for
7 papers · 1 filter
On the origin of the anomalous precession of Mercury's perihelion
Jaume Giné
Action at distance in Newtonian physics is replaced by finite propagation speeds in classical post--Newtonian physics. As a result, the differential equations of motion in Newtonia…
On the origin of the gravitational quantization: The Titius--Bode Law
Jaume Giné
Action at distance in Newtonian physics is replaced by finite propagation speeds in classical post--Newtonian physics. As a result, the differential equations of motion in Newtonia…
A note on "Relaxation Oscillators with Exact Limit Cycles"
Jaume Giné, Maite Grau
In this note we give a family of planar polynomial differential systems with a prescribed hyperbolic limit cycle. This family constitutes a corrected and wider version of an exampl…
The role of algebraic solutions in planar polynomial differential systems
Héctor Giacomini, Jaume Giné, Maite Grau
We study a planar polynomial differential system, given by \dot{x}=P(x,y), \dot{y}=Q(x,y). We consider a function I(x,y)=\exp \{h_2(x) A_1(x,y) \diagup A_0(x,y) \} h_1(x) \prod_{i=…
Integrability of planar polynomial differential systems through linear differential equations
Héctor Giacomini, Jaume Giné, Maite Grau
In this work, we consider rational ordinary differential equations dy/dx = Q(x,y)/P(x,y), with Q(x,y) and P(x,y) coprime polynomials with real coefficients. We give a method to con…
The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems
Héctor Giacomini, Jaume Giné, Jaume Llibre
In this work we study the centers of planar analytic vector fields which are limit of linear type centers. It is proved that all the nilpotent centers are limit of linear type cent…
On the origin of quantum mechanics
Jaume Giné
Action at distance in Newtonian physics is replaced by finite propagation speeds in classical post--Newtonian physics. As a result, the differential equations of motion in Newtonia…