Tootfinder

A Novel Four-Stage Synchronized Chaotic Map: Design and Statistical Characterization
Ricardo Francisco Martinez-Gonzalez
https://arxiv.org/abs/2507.03635 h…

A Novel Four-Stage Synchronized Chaotic Map: Design and Statistical Characterization
Digital implementations of chaotic systems often suffer from inherent degradation, limiting their long-term performance and statistical quality. To address this challenge, we propose a novel four-stage synchronized piecewise linear chaotic map. This new map is meticulously designed with four independent segments, each possessing its own control parameters, specifically engineered to mitigate the natural degradation observed in digitally realized dynamical systems. We characterize its behavior u…

Quasi-isospectral higher-order Hamiltonians via a reversed Lax pair construction
Francisco Correa, Andreas Fring
https://arxiv.org/abs/2507.19622 https://a…

Quasi-isospectral higher-order Hamiltonians via a reversed Lax pair construction
We present a novel approach for constructing quasi-isospectral higher-order Hamiltonians from time-independent Lax pairs by reversing the conventional interpretation of the Lax pair operators. Instead of treating the typically second-order $L$-operator as the Hamiltonian, we take the higher-order $M$-operator as the starting point and construct a sequence of quasi-isospectral operators via intertwining techniques. This procedure yields a variety of new higher-order Hamiltonians that are isospec…

Shearless barriers in the conservative Ikeda map
Rodrigo Simile Baroni, Ricardo Egydio de Carvalho, Jos\'e Danilo Szezech Junior, Iber\^e Luiz Caldas
https://arxiv.org/abs/2507.07322

Shearless barriers in the conservative Ikeda map
We investigate the dynamics of the Ikeda map in the conservative limit, where it is represented as a two-dimensional area-preserving map governed by two control parameters, $θ$ and $ϕ$. We demonstrate that the map can be interpreted as a composition of a rotation and a translation of the state vector. In the integrable case ($ϕ= 0$), the map reduces to a uniform rotation by angle $θ$ about a fixed point, independent of initial conditions. For $ϕ\ne 0$, the system becomes nonintegrable, and…