Related Experiment Video
Updated: Jun 5, 2026

Controlling the Size, Shape and Stability of Supramolecular Polymers in Water
Published on: August 2, 2012
On structural stability of 3-diffeomorphisms with the Smale solenoid attractor-repeller dynamics
1Faculty of Informatics, Mathematics, and Computer Science (HSE Nizhny Novgorod), HSE University, Nizhny Novgorod, Russia.
None:
We consider 3-diffeomorphisms with source-sink dynamics where Smale solenoids play the role of the source and the sink (NSSS-diffeomorphisms). It is known that such diffeomorphisms exist only on lens spaces. On the 3-sphere, every NSSS-diffeomorphism is associated with an exchangeable braid. An exchangeable braid with the strand number n was constructed for each n ⩾ 3 in such a way that the NSSS-diffeomorphism on S3 realized for this braid is not structurally stable. The braid of the classic Smale's example has the strand number 2 and is exchangeable and the technique for n ⩾ 3 cannot be applied to prove that the corresponding NSSS-diffeomorphism on S3 is not structurally stable. This paper aims to fill this gap.
Related Concept Videos
Stability of Equilibrium Configuration: Problem Solving
Problem-solving in the context of the stability of equilibrium configuration...
Stability of structures
Stability of Equilibrium Configuration
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
Pole and System Stability
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
Statically Indeterminate Problem Solving
One-Degree-of-Freedom System
A one-degree-of-freedom system is defined by an independent variable that determines its state and behavior. One example of a one-degree-of-freedom system is a simple harmonic oscillator, such as a...