LAUSR

Persistence of Degenerate Lower Dimensional Invariant Tori with Prescribed Frequencies in Reversible Systems

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0 Published in 2021 at "Journal of Dynamics and Differential Equations"

DOI: 10.1007/s10884-021-09989-x

Abstract: This paper considers small perturbations of an integrable reversible system which has a degenerated lower dimensional invariant torus in some sense. In the presence of some higher-order terms, by some KAM technique and the stability… read more here.

Keywords: prescribed frequencies; lower dimensional; persistence degenerate; reversible systems ... See more keywords

One-dimensional invariant measure in periodicity hubs: A tribute to Professor Jason A. C. Gallas.

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0 Published in 2025 at "Chaos"

DOI: 10.1063/5.0239023

Abstract: Chaotic behavior near a periodicity hub is characterized in five different three-dimensional systems, namely, the paradigmatic Rössler system, the Rosenzweig-MacArthur predator-prey model, a semiconductor laser model, the Gaspard-Nicolis chemical oscillator, and the Nishio-Inaba electronic circuit.… read more here.

Keywords: dimensional invariant; periodicity; measure periodicity; periodicity hubs ... See more keywords

Persistence of lower dimensional invariant tori in a class of reversible systems

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0 Published in 2018 at "Dynamical Systems"

DOI: 10.1080/14689367.2017.1298725

Abstract: ABSTRACT In this paper we prove the persistence of lower dimensional invariant tori for a class of reversible systems without any non-degeneracy condition. In the proof, we use the special nature that the dimension of… read more here.

Keywords: lower dimensional; invariant tori; persistence lower; dimensional invariant ... See more keywords

Persistence of Hyperbolic-type Degenerate Lower-dimensional Invariant Tori with Prescribed Frequencies in Hamiltonian Systems

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0 Published in 2020 at "Regular and Chaotic Dynamics"

DOI: 10.1134/s1560354720060088

Abstract: It is known that under Kolmogorov’s nondegeneracy condition, the nondegenerate hyperbolic invariant torus with Diophantine frequencies will persist under small perturbations, meaning that the perturbed system still has an invariant torus with prescribed frequencies. However,… read more here.

Keywords: prescribed frequencies; lower dimensional; hyperbolic type; type degenerate ... See more keywords