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ЖУРНАЛЫ // Regular and Chaotic Dynamics // Архив

Regul. Chaotic Dyn., 2025, том 30, выпуск 2, страницы 174–187 (Mi rcd1303)

A Geometric Model for Pseudohyperbolic Shilnikov Attractors

Dmitry Turaev

Imperial College, SW7 2AZ London, UK

Аннотация: We describe a $C^1$-open set of systems of differential equations in $R^n$, for any $n\geqslant 4$, where every system has a chain-transitive chaotic attractor which contains a saddle-focus equilibrium with a two-dimensional unstable manifold. The attractor also includes a wild hyperbolic set and a heterodimensional cycle involving hyperbolic sets with different numbers of positive Lyapunov exponents.

Ключевые слова: saddle-focus, homoclinic loop, spiral chaos

Поступила в редакцию: 06.01.2025
Принята в печать: 12.03.2025

Язык публикации: английский

DOI: 10.1134/S1560354725020029



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