Zobrazeno 1 - 10
of 416
pro vyhledávání: '"37C29"'
Autor:
Igra, Eran
We study the dynamics of the Nose-Hoover and Moore-Spiegel Oscillators, and in particular, their topological dynamics. We prove the dynamics of both these systems can be reduced to a flow on a solid torus, with at most a finite number of attracting p
Externí odkaz:
http://arxiv.org/abs/2409.16624
Autor:
Sander, E., Meiss, J. D.
The Lyapunov exponents of a dynamical system measure the average rate of exponential stretching along an orbit. Positive exponents are often taken as a defining characteristic of chaotic dynamics. However, the standard orthogonalization-based method
Externí odkaz:
http://arxiv.org/abs/2409.08496
Quorum sensing orchestrates bacterial communication, which is vital for bacteria's population behaviour. We propose a mathematical model that unveils chaotic dynamics within quorum sensing networks, challenging predictability. The model considers the
Externí odkaz:
http://arxiv.org/abs/2409.02764
In traffic flow, self-organized wave propagation, which characterizes congestion, has been reproduced in macroscopic and microscopic models. Hydrodynamic models, a subset of macroscopic models, can be derived from microscopic-level car-following mode
Externí odkaz:
http://arxiv.org/abs/2406.13293
Autor:
Li, Dongchen
The aim of this paper is twofold. First, motivated by the nearly-affine blender system found in [LT24], we introduce standard blenders and their variations, and prove their fundamental properties on the generation of $C^1$-robust tangencies. Next, as
Externí odkaz:
http://arxiv.org/abs/2406.12500
In the paper, we utilize the recent variational, abstract theorem to show the existence of homoclinic solutions to the Hamiltonian system $$ \dot{z} = J D_z H(z, t), \quad t \in \mathbb{R}, $$ where the Hamiltonian $H : \mathbb{R}^{2N} \times \mathbb
Externí odkaz:
http://arxiv.org/abs/2405.20908
We introduce the concept of a heterodimensional cycle of hyperbolic ergodic measures and a special type of them that we call rich. Within a partially hyperbolic context, we prove that if two measures are related by a rich heterodimensional cycle, the
Externí odkaz:
http://arxiv.org/abs/2405.12686
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
This paper proposes a new concept of pluripotency inspired by Colli-Vargas [Ergod. Theory Dyn. Syst., 21(6):1657-1681, 2001] and presents fundamental theorems for developing the theory. Pluripotency reprograms dynamics from a statistical or geometric
Externí odkaz:
http://arxiv.org/abs/2404.00337
Autor:
Li, Dongchen
Blenders are special hyperbolic sets used to produce various robust dynamical phenomena which appear fragile at first glance. We prove for $C^r$ diffeomorphisms ($r=2,\dots,\infty,\omega$) that blenders naturally exist (without perturbation) near non
Externí odkaz:
http://arxiv.org/abs/2403.15818