arXiv subjects

Jesús San Martín

Publications and source records attributed to Jesús San Martín.

6 recordsLinked to original sources

arXiv2026

Quasi-Sierpinski Structure for Uniform Load Distribution

Land reclamation methods, indispensable for the proper development of modern coastal cities, are ecologically destructive. We present a fractal structure, similar to a Sierpinski triangle, which solves this problem by resting directly on the seabed thanks to the uniform load distribution we achieve on its base. To obtain this uniform distribution, we show that the supports of the structure must displace vertically following any function of the Takagi class. This causes the vertical deformations of the structure to follow this same class and the horizontal deformations to be related to the Cantor function. The structure works with an unlimited number of combinations of areas of its elements and materials, which gives designers a high degree of constructive flexibility.

math-ph↗

arXiv2020

The Takagi Curve and the $β$-Cantor Function from Mechanical Laws

This work shows that fractals can be obtained from Mechanical Laws without being forced by any algorithm, closing the gap between the Platonic world of Mathematics and Nature. Fractal tree crown directly emerges when applying elasticity theory to branching stresses in a binary tree. Vertical displacements of nodes are given by the Takagi curve, while the horizontal ones are given by a linear combination of inverses of $β$-Cantor functions. In addition, both fractal dimensions are related, which suggests a deeper connection between the Takagi Curve and the $β$-Cantor function.

math.DS↗

arXiv2018

The morphology of MSS-sequences in a wide class of unimodal maps, its structure and decomposition

The MSS-sequences (U-sequences) in a wide class of unimodal maps have the look $\mathrm{P}=(\mathrm{R} \mathrm{L}^{q})^{n_1} \mathrm{S}_1(m_1,q-1) (\mathrm{R} \mathrm{L}^{q})^{n_2}\mathrm{S}_2(m_2,q-1) $ $\ldots$ $ (\mathrm{R} \mathrm{L}^{q})^{n_r}$ $ \mathrm{S}_r(m_r,q-1)\mathrm{C},$ where $\mathrm{S}_i(m_i, q-1)$ are sequences of $\mathrm{R}$s and $\mathrm{L}$s that contain at most $q-1$ consecutive $\mathrm{L}$s. The first block $\mathrm{RL}^q$ and the sequence $\mathrm{S}_1$ following it are essential for an admissible sequence to be a MSS-sequence. Moreover $\mathrm{S}_i(m_i,q-1), \ i=2, \ldots, r$ are determined by $\mathrm{S}_1(m_1,q-1)$. Explicit structure of MSS-sequences will be given as well as the theorems that decompose the non-primary MSS-sequences. The cardinality will be calculated for some important sets of non-primary MSS-sequences and an algorithm to generate the blocks $\mathrm{S}_i(m_i,q-1), \ i=1, \ldots, r$ will be provided, as the construction of the blocks $\mathrm{S}_i(m_i,q-1)$ allows the construction of the MSS-sequences.

math.DS↗

arXiv2015

Heterogeneous, Weakly Coupled Map Lattices

Coupled map lattices (CMLs) are often used to study emergent phenomena in nature. It is typically assumed (unrealistically) that each component is described by the same map, and it is important to relax this assumption. In this paper, we characterize periodic orbits and the laminar regime of type-I intermittency in heterogeneous weakly coupled map lattices (HWCMLs). We show that the period of a cycle in an HWCML is preserved for arbitrarily small coupling strengths even when an associated uncoupled oscillator would experience a period-doubling cascade. Our results characterize periodic orbits both near and far from saddle--node bifurcations, and we thereby provide a key step for examining the bifurcation structure of heterogeneous CMLs.

nlin.PS↗

arXiv2014

Convergence Time Towards Periodic Orbits in Discrete Dynamical Systems

We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we use linearized equations to examine the evolution near that neighborhood. The underlying idea is that points of stable periodic orbit are associated with intervals. We state and prove a theorem that details what regions of phase space are mapped into these intervals (once they are known) and how many iterations are required to get there. We also construct algorithms that allow our theoretical results to be implemented successfully in practice.

math.DS↗

arXiv2014

Compound orbits break-up in constituents: an algorithm

In this paper decomposition of periodic orbits in bifurcation diagrams are derived in unidimensional dynamics system $x_{n+1}=f(x_{n};r)$, being $f$ an unimodal function. We proof a theorem which states the necessary and sufficient conditions for the break-up of compound orbits in their simpler constituents. A corollary to this theorem provides an algorithm for the computation of those orbits. This process closes the theoretical framework initiated in (Physica D, 239:1135--1146, 2010).

nlin.CD↗