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pro vyhledávání: '"Garijo, Antonio"'
In this paper we give analytic proofs of the existence of transversal homoclinic points for a family of non-globally smooth diffeomorphisms having the origin as a fixed point which come out as a truncated map governing the local dynamics near a criti
Externí odkaz:
http://arxiv.org/abs/2405.08812
We consider the secant method $S_p$ applied to a real polynomial $p$ of degree $d+1$ as a discrete dynamical system on $\mathbb R^2$. If the polynomial $p$ has a local extremum at a point $\alpha$ then the discrete dynamical system generated by the i
Externí odkaz:
http://arxiv.org/abs/2405.08791
In this paper we study a one parameter family of rational maps obtained by applying the Chebyshev-Halley root finding algorithms. We show that the dynamics near parameters where the family presents some degeneracy might be understood from the point o
Externí odkaz:
http://arxiv.org/abs/2401.12374
Publikováno v:
Chaos, Solitons & Fractals 166 (2023) 112921
The dynamics of many epidemic compartmental models for infectious diseases that spread in a single host population present a second-order phase transition. This transition occurs as a function of the infectivity parameter, from the absence of infecte
Externí odkaz:
http://arxiv.org/abs/2210.17156
Autor:
Dias, Kealey, Garijo, Antonio
We consider the rational flow $\xi_R(z)= R(z) (d/dz)$ where $R$ is given by the quotient of two polynomials without common factors on the Riemann sphere. The separatrix graph $\Gamma_R$ is the boundary between trajectories with different properties.
Externí odkaz:
http://arxiv.org/abs/2010.00066
We study the discrete dynamical system defined on a subset of $R^2$ given by the iterates of the secant method applied to a real polynomial $p$. Each simple real root $\alpha$ of $p$ has associated its basin of attraction $\mathcal A(\alpha)$ formed
Externí odkaz:
http://arxiv.org/abs/2006.01528
Akademický článek
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Autor:
Garijo, Antonio, Jarque, Xavier
We investigate the plane dynamical system given by the secant map applied to a polynomial $p$ having at least one multiple root of multiplicity $d>1$. We prove that the local dynamics around the fixed points associated to the roots of $p$ depend on t
Externí odkaz:
http://arxiv.org/abs/1907.09323
Autor:
Garijo, Antonio, Jarque, Xavier
We investigate the root finding algorithm given by the secant method applied to a real polynomial $p$ as a discrete dynamical system defined on $\mathbb R^2$. We study the shape and distribution of the basins of attraction associated to the roots of
Externí odkaz:
http://arxiv.org/abs/1812.10954
Publikováno v:
In Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena January 2023 166