Ergodic Measures with Multi-zero Lyapunov Exponents Inside Homoclinic Classes
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Dynamics and Differential Equations"
DOI: 10.1007/s10884-019-09752-3
Abstract: In this paper, we prove that for $$C^1$$ C 1 -generic diffeomorphisms, if a homoclinic class contains periodic orbits of indices i and j with $$j>i+1$$ j > i + 1 , and the homoclinic… read more here.
Keywords: ergodic measures; homoclinic class; multi zero; measures multi ... See more keywords
On the origin of chaotic attractors with two zero Lyapunov exponents in a system of five biharmonically coupled phase oscillators.
Sign Up to like & getrecommendations! Published in 2022 at "Chaos"
DOI: 10.1063/5.0098163
Abstract: We study chaotic dynamics in a system of four differential equations describing the interaction of five identical phase oscillators coupled via biharmonic function. We show that this system exhibits strange spiral attractors (Shilnikov attractors) with… read more here.
Keywords: system; phase oscillators; attractors two; zero lyapunov ... See more keywords
Zero Lyapunov exponents and monodromy of the Kontsevich–Zorich cocycle
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DOI: 10.1215/00127094-3715806
Abstract: We describe all the situations in which the Kontsevich-Zorich cocycle has zero Lyapunov exponents. Confirming a conjecture of Forni, Matheus, and Zorich, this only occurs when the cocycle satisfies additional geometric constraints. We also describe… read more here.
Keywords: monodromy kontsevich; zorich cocycle; cocycle; kontsevich zorich ... See more keywords