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Dive into the research topics where J. Tomás Lázaro is active.

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Featured researches published by J. Tomás Lázaro.


Qualitative Theory of Dynamical Systems | 2002

A pseudo-normal form for planar vector fields

Amadeu Delshams; Antoni Guillamon; J. Tomás Lázaro

The pseudo-normal form is presented as an alternative to the Birkhoff normal form for a planar vector field with the origin as an equilibrium point. Its convergence is proved for non-zero critical exponents λ,−λ, and some consequences for the center-focus, problem are presented.


Archive | 1999

Effective Stability in Reversible Systems

Amadeu Delshams; J. Tomás Lázaro

It is difficult, in the theory of dynamical systems, to draw a boundary line between conservation laws and symmetries because often their effects on the dynamics can be almost the same. An important example can be the case of motions in Hamiltonian and reversible systems. For instance, it is well-known that the Kolmogorov-Arnol’d-Moser theory applies in both type of systems (see [1, 2, 12, 11]). In the theory of Hamiltonian systems we also have the Nekhoroshev theorem [7], that leads to the concept of effective stability.


Journal of Theoretical Biology | 2019

Viral replication modes in single-peak fitness landscapes: A dynamical systems analysis

Joan Fornés; J. Tomás Lázaro; Tomás Alarcón; Santiago F. Elena; Josep Sardanyés

Positive-sense, single-stranded RNA viruses are important pathogens infecting almost all types of organisms. Experimental evidence from distributions of mutations and from viral RNA amplification suggest that these pathogens may follow different RNA replication modes, ranging from the stamping machine replication (SMR) to the geometric replication (GR) mode. Although previous theoretical work has focused on the evolutionary dynamics of RNA viruses amplifying their genomes with different strategies, little is known in terms of the bifurcations and transitions involving the so-called error threshold (mutation-induced dominance of mutants) and lethal mutagenesis (extinction of all sequences due to mutation accumulation and demographic stochasticity). Here we analyze a dynamical system describing the intracellular amplification of viral RNA genomes evolving on a single-peak fitness landscape focusing on three cases considering neutral, deleterious, and lethal mutants. We analytically derive the critical mutation rates causing lethal mutagenesis and error threshold, governed by transcritical bifurcations that depend on parameters α (parameter introducing the mode of replication), replicative fitness of mutants (k1), and on the spontaneous degradation rates of the sequences (ϵ). Our results relate the error catastrophe with lethal mutagenesis in a model with continuous populations of viral genomes. The former case involves dominance of the mutant sequences, while the latter, a deterministic extinction of the viral RNAs during replication due to increased mutation. For the lethal case the critical mutation rate involving lethal mutagenesis is μc=1-ɛ/α. Here, the SMR involves lower critical mutation rates, being the system more robust to lethal mutagenesis replicating closer to the GR mode. This result is also found for the neutral and deleterious cases, but for these later cases lethal mutagenesis can shift to the error threshold once the replication mode surpasses a threshold given by α=ϵ/k1.


Proceedings of the International Conference | 2001

PSEUDO-NORMAL FORMS AND THEIR APPLICATIONS

Amadeu Delshams; J. Tomás Lázaro

Since they were introduced by Poincare in his thesis, Normal Forms have become a common and useful tool in the local qualitative study of dynamical systems. Consequently, the literature about this subject is very rich, not only because of the people working on it (Poincare, Dulac, Birkhoff, Stenberg, Chen, Arnold, Moser, Tokarev, Bibikov, Belitskǐi, Bruno, Walcher, Cicogna, Gaeta, Bambusi and many others) but the also the amount of publications (see, for instance 1,2,6,3,7 and references therein). Let us consider a real planar analytic system


Nonlinear Analysis-theory Methods & Applications | 2012

Upper bounds for the number of zeroes for some Abelian integrals

Armengol Gasull; J. Tomás Lázaro; Joan Torregrosa


Discrete and Continuous Dynamical Systems | 2014

On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory

Primitivo B. Acosta-Humánez; J. Tomás Lázaro; Juan J. Morales-Ruiz; Chara Pantazi


Journal of Mathematical Analysis and Applications | 2012

On the Chebyshev property for a new family of functions

Armengol Gasull; J. Tomás Lázaro; Joan Torregrosa


Journal of Differential Equations | 2005

Pseudo-normal form near saddle-center or saddle-focus equilibria

Amadeu Delshams; J. Tomás Lázaro


Computational & Applied Mathematics | 2017

Dynamics and bifurcations in a simple quasispecies model of tumorigenesis

Vanessa Castillo; J. Tomás Lázaro; Josep Sardanyés


arXiv: Dynamical Systems | 2018

Mixed dynamics of 2-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies

Amadeu Delshams; Marina Gonchenko; S. V. Gonchenko; J. Tomás Lázaro

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Dive into the J. Tomás Lázaro's collaboration.

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Amadeu Delshams

Polytechnic University of Catalonia

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Antoni Guillamon

Polytechnic University of Catalonia

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Armengol Gasull

Autonomous University of Barcelona

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Chara Pantazi

Polytechnic University of Catalonia

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Joan Torregrosa

Autonomous University of Barcelona

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Juan J. Morales-Ruiz

Technical University of Madrid

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Joan Fornés

Polytechnic University of Catalonia

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