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The onset of chaos in one-dimensional spinning particle models derived from pseudoclassical mechanical hamiltonians with a bosonic Duffing potential is examined. Using the Melnikov method, we indicate the presence of homoclinic…

Chaotic Dynamics · Physics 2009-11-07 H. T. Cho , J. -K. Kao

We prove a Simons-type holonomy theorem for totally skew 1-forms with values in a Lie algebra of linear isometries. The only transitive case, for this theorem, is the full orthogonal group. We only use geometric methods and we do not use…

Differential Geometry · Mathematics 2008-11-26 Carlos Olmos , Silvio Reggiani

The Turing-Hopf type spatiotemporal patterns in a diffusive Holling-Tanner model with discrete time delay is considered. A global Turing bifurcation theorem for $\tau=0$ and a local Turing bifurcation theorem for $\tau>0$ are given by the…

Dynamical Systems · Mathematics 2019-01-30 Qi An , Weihua Jiang

We investigate the emergence of chaotic dynamics in collective-coordinate reductions of a driven and spatially modulated $\phi^4$ field describing the motion of topological kinks. Focusing on finite-dimensional effective models, we consider…

Pattern Formation and Solitons · Physics 2026-05-26 Vassilios M Rothos

The concept of sliding Shilnikov connection has been recently introduced and represents an important notion in Filippov systems, because its existence implies chaotic behavior on an invariant subset of the system. The investigation of its…

Dynamical Systems · Mathematics 2024-11-18 Matheus G. C. Cunha , Douglas D. Novaes , Gabriel Ponce

We prove that if a Hamiltonian diffeomorphism of a closed monotone symplectic manifold with semisimple quantum homology has more contractible fixed points, counted homologically, than the total dimension of the homology of the manifold,…

Symplectic Geometry · Mathematics 2019-11-22 Egor Shelukhin

We study the action of Bogoliubov transformations on admissible generalized one-particle density matrices arising in Hartree-Fock-Bogoliubov theory. We show that the orbits of this action are reductive homogeneous spaces, and we give…

Functional Analysis · Mathematics 2024-02-27 Claudia D. Alvarado , Eduardo Chiumiento

This paper addresses the perturbation of higher-dimensional non-smooth autonomous differential systems characterized by two zones separated by a codimension-one manifold, with an integral manifold foliated by crossing periodic solutions.…

Dynamical Systems · Mathematics 2024-09-04 Oscar A. R. Cespedes , Douglas D. Novaes

This article concerns arbitrary finite heteroclinic networks in any phase space dimension whose vertices can be a random mixture of equilibria and periodic orbits. In addition, tangencies in the intersection of un/stable manifolds are…

Dynamical Systems · Mathematics 2010-04-28 Jens D. M. Rademacher

We revisit the classical Suarez-Schopf delayed oscillator. Special attention is paid to the region of linear stability in the space of parameters. By means of the theory of inertial manifolds developed in our adjacent papers, we provide…

Dynamical Systems · Mathematics 2024-02-08 Mikhail Anikushin , Andrey Romanov

We consider two stable heteroclinic cycles rotating in opposite directions, coupled via diffusive terms. A complete synchronization in this system is impossible, and numerical exploration shows that chaos is abundant at low levels of…

Chaotic Dynamics · Physics 2023-06-14 Arkady Pikovsky , Alexander Nepomnyashchy

The unified product was defined in \cite{am3} related to the restricted extending structure problem for Hopf algebras: a Hopf algebra $E$ factorizes through a Hopf subalgebra $A$ and a subcoalgebra $H$ such that $1\in H$ if and only if $E$…

Rings and Algebras · Mathematics 2014-02-24 A. L. Agore , G. Militaru

The goal of this paper is twofold. In addition to the results stated in the next paragraph, we present some classical results on absoluteness relevant to functional analysis that are well known to logicians but not nearly as well advertised…

Operator Algebras · Mathematics 2026-02-18 Bruce Blackadar , Ilijas Farah

This paper investigates the local behavior of 3D Filippov systems $Z=(X,Y)$, focusing on the dynamics around cusp-fold singularities. These singular points, characterized by cubic contact of vector field $X$ and quadratic contact of vector…

Dynamical Systems · Mathematics 2025-07-15 Oscar A. R. Cespedes , Rony Cristiano , Otávio M. L. Gomide

In this paper we study the appearance of branches of relative periodic orbits in Hamiltonian Hopf bifurcation processes in the presence of compact symmetry groups that do not generically exist in the dissipative framework. The theoretical…

Dynamical Systems · Mathematics 2009-11-07 Pascal Chossat , Juan-Pablo Ortega , Tudor S. Ratiu

This Thesis explores the notion of Krylov complexity as a probe of quantum chaos and as a candidate for holographic complexity. The first Part is devoted to presenting the fundamental notions required to conduct research in this area.…

High Energy Physics - Theory · Physics 2024-07-08 A. Sánchez-Garrido

In 2002 Polterovich has notably established that on closed aspherical symplectic manifolds, Hamiltonian diffeomorphisms of finite order, which we call Hamiltonian torsion, must in fact be trivial. In this paper we prove the first…

Symplectic Geometry · Mathematics 2020-09-09 Marcelo S. Atallah , Egor Shelukhin

This is a long overdue write up of the following: If the fundamental group of a normal complex algebraic variety (respectively Zariski open subset of a compact K\"ahler manifold) is a solvable group of matrices over Q (respectively…

alg-geom · Mathematics 2016-08-30 Donu Arapura , Madhav Nori

We give a hydrodynamical explanation for the chaotic behaviour of a dripping faucet using the results of the stability analysis of a static pendant drop and a proper orthogonal decomposition (POD) of the complete dynamics. We find that the…

Fluid Dynamics · Physics 2009-11-10 P. Coullet , L. Mahadevan , C. S. Riera

We consider analytical formulae that describe the chaotic regions around the main periodic orbit $(x=y=0)$ of the H\'{e}non map. Following our previous paper (Efthymiopoulos, Contopoulos, Katsanikas $2014$) we introduce new variables $(\xi,…

Chaotic Dynamics · Physics 2015-06-23 M. Harsoula , G. Contopoulos , C. Efthymiopoulos