Positive Ricci curvature through Cheeger deformations

F., Cavenaghi, Leonardo; Silva, Renato J.M. e; Sperança, Llohann D.

doi:10.1007/s13348-023-00396-7

Cited by 3 publications

(4 citation statements)

References 29 publications

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“…1 shows an schematic illustration example of a typical flow within slow-fast dynamical systems for m = n = 1. The figure is the case of van der Pol equation which is a most classical [6] slow-fast dynamical system. We consider f to be cubic function which is a type of y 3 and g to be a linear function.…”

Section: Slow-fast Dynamical Systemsmentioning

confidence: 99%

“…One of the notable phenomena in slow-fast dynamical systems is the canard solution [6]. The canard solution occurs when the equilibrium point on C 0,r transitions to a relaxation oscillation via a Hopf bifurcation.…”

Section: Slow-fast Dynamical Systemsmentioning

confidence: 99%

“…This indicates that the system is bistable when the parameter is between the tangent bifurcation and the Hopf bifurcation. The van der Pol oscillator represents a typical slow-fast dynamical system [6]. In the original van der Pol equation [10], a vacuum tube amplifier is used, resulting in a critical manifold of sigmoid shape.…”

Section: Slow-fast Dynamical Systemsmentioning

confidence: 99%

“…A notable phenomenon observed in slow-fast dynamics is the canard [6]. Canards occur only in a very limited range of parameters immediately prior to an amplitude explosion [4], [7].…”

Section: Introductionmentioning

confidence: 99%

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Transient Responses to Relaxation Oscillations in Multivibrators

Amoh,

Ueta,

Kawakami

2024

IEEE Access

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The multivibrator is an electronic circuit that has three oscillation states: astable, monostable, and bistable; these circuits typically contain opamps. These states are often modeled using hybrid systems, which contain characteristics of both continuous and discrete time. While an ideal opamp possesses both continuous and discrete characteristics, actual opamps exhibit continuous properties, which necessitate indepth modeling. The relaxation oscillations produced by the multivibrator, characterized by periodic, rapid state changes, are typically modeled by considering slow-fast dynamical systems. In these systems, the phenomenon whereby the amplitude of the signal changes rapidly is referred to as a ''canard explosion''. By considering this phenomenon, it is possible to understand the process of relaxation oscillations in the multivibrator. In this work, we model the multivibrator by considering a slow-fast dynamical system and observe canard explosions through numerical experiments. This study indicates that the oscillatory changes in the multivibrator are continuous, which explains the onset of relaxation oscillations. Additionally, circuit experiments are conducted using affordable opamps; in this experimental work, canard explosions are observed.

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Section: Slow-fast Dynamical Systemsmentioning

confidence: 99%

Section: Slow-fast Dynamical Systemsmentioning

confidence: 99%

Section: Slow-fast Dynamical Systemsmentioning

confidence: 99%

“…A notable phenomenon observed in slow-fast dynamics is the canard [6]. Canards occur only in a very limited range of parameters immediately prior to an amplitude explosion [4], [7].…”

Section: Introductionmentioning

confidence: 99%

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Transient Responses to Relaxation Oscillations in Multivibrators

Amoh,

Ueta,

Kawakami

2024

IEEE Access

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Gromoll–Meyer's actions and the geometry of (exotic) spacetimes

Cavenaghi,

Grama

2024

Differential Geometry and its Applications

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The Symmetric Kazdan–warner Problem and Applications

Sperança

2022

Preprint

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After R. Schoen completed the solution of the Yamabe problem, compact manifolds could be categorized in three classes, depending on whether they admit a metric with positive, non-negative, or only negative scalar curvature. Here we follow Yamabe’s first attempt to solve his problem through variational methods and provide an analogous equivalent classification for manifolds equipped with actions by non-discrete compact Lie groups. Moreover, we apply the method and the results to: classify total spaces of fiber bundles with compact structure groups (concerning scalar curvature), to conclude density results and compare realizable scalar curvature functions between some exotic manifolds and their standard counterpart. We also provide an extended range of prescribed scalar curvature functions of warped products, especially with Calabi–Yau manifolds.

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Positive Ricci curvature through Cheeger deformations

Cited by 3 publications

References 29 publications

Transient Responses to Relaxation Oscillations in Multivibrators

Transient Responses to Relaxation Oscillations in Multivibrators

Gromoll–Meyer's actions and the geometry of (exotic) spacetimes

The Symmetric Kazdan–warner Problem and Applications

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