Qualitative Theory of Dynamical Systems· 2026Q1
Sliding Trajectories of Generic Inelastic Piecewise-Linear Dynamical Systems on the Torus
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- Q1SCImago
- 2026year
Short summary
Generic inelastic piecewise-linear dynamical systems on a torus exhibit closed sliding trajectories, with tangency sets classified and topological equivalence established.
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Key points
- Classifies the tangency set on the torus for inelastic piecewise-linear dynamical systems.
- Describes the dynamics of the associated sliding vector field.
- Proves that generic sliding trajectories on the torus are closed.
- Establishes a result on the topological equivalence of inelastic vector fields on the torus.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract We consider piecewise smooth differential equations $$Z_{X_-X_+}$$ Z X - X + , where $$X_-$$ X - and $$X_+$$ X + are linear inelastic vector fields on $$\mathbb {R}^3$$ R 3 with the torus as the discontinuity manifold. Under suitable assumptions, we classify the tangency set on the torus and describe the dynamics of the associated sliding vector field. We prove that, under generic conditions, every trajectory of the sliding vector field on the torus is closed. Finally, we establish a result on the topological equivalence of inelastic vector fields on the torus.
The authors' abstract, as published at the source. Qualitative Theory of Dynamical Systems, 2026 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics