Hamiltonian dynamics, classical R-matrices and isomonodromic deformations

AbstractWe study the relation between class $$\mathcal {S}$$ S theories on punctured tori and isomonodromic deformations of flat SL(N) connections on the two-dimensional torus with punctures. Turning on the self-dual $$\Omega $$ Ω -background corresponds to a deautonomization of the Seiberg–Witten integrable system which implies a specific time dependence in its Hamiltonians. We show that the corresponding $$\tau $$ τ -function is proportional to the dual gauge theory partition function, the proportionality factor being a nontrivial function of the solution of the deautonomized Seiberg–Witten integrable system. This is obtained by mapping the isomonodromic deformation problem to $$W_N$$ W N free fermion correlators on the torus.

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Forecasting Hamiltonian dynamics without canonical coordinates

Nonlinear Dynamics ◽

10.1007/s11071-020-06185-2 ◽

2021 ◽

Author(s):

Anshul Choudhary ◽

John F. Lindner ◽

Elliott G. Holliday ◽

Scott T. Miller ◽

Sudeshna Sinha ◽

...

Keyword(s):

Hamiltonian Dynamics ◽

Canonical Coordinates

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Bifurcation analysis of nonlinear Hamiltonian dynamics in the Fermilab Integrable Optics Test Accelerator

Physical Review Accelerators and Beams ◽

10.1103/physrevaccelbeams.23.064002 ◽

2020 ◽

Vol 23 (6) ◽

Cited By ~ 1

Author(s):

Chad E. Mitchell ◽

Robert D. Ryne ◽

Kilean Hwang

Keyword(s):

Bifurcation Analysis ◽

Hamiltonian Dynamics

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DYNAMICAL METEOROLOGY | Hamiltonian Dynamics

Encyclopedia of Atmospheric Sciences ◽

10.1016/b978-0-12-382225-3.00008-6 ◽

2015 ◽

pp. 324-331 ◽

Cited By ~ 1

Author(s):

T.G. Shepherd

Keyword(s):

Hamiltonian Dynamics

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On squaring the primary constraints in a generalized Hamiltonian dynamics

Physics Letters B ◽

10.1016/0370-2693(94)91527-x ◽

1994 ◽

Vol 327 (1-2) ◽

pp. 50-55 ◽

Cited By ~ 11

Author(s):

V.V. Nesterenko

Keyword(s):

Hamiltonian Dynamics

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Hamiltonian Chaos in a Model Alveolus

Journal of Biomechanical Engineering ◽

10.1115/1.2953559 ◽

2008 ◽

Vol 131 (1) ◽

Cited By ~ 13

Author(s):

F. S. Henry ◽

F. E. Laine-Pearson ◽

A. Tsuda

Keyword(s):

Reynolds Number ◽

Fixed Point ◽

Lyapunov Exponent ◽

Fine Particles ◽

Hamiltonian Dynamics ◽

Maximal Lyapunov Exponent ◽

Poincaré Sections ◽

Pulmonary Acinus ◽

Hamiltonian Chaos ◽

Poincare Sections

In the pulmonary acinus, the airflow Reynolds number is usually much less than unity and hence the flow might be expected to be reversible. However, this does not appear to be the case as a significant portion of the fine particles that reach the acinus remains there after exhalation. We believe that this irreversibility is at large a result of chaotic mixing in the alveoli of the acinar airways. To test this hypothesis, we solved numerically the equations for incompressible, pulsatile, flow in a rigid alveolated duct and tracked numerous fluid particles over many breathing cycles. The resulting Poincaré sections exhibit chains of islands on which particles travel. In the region between these chains of islands, some particles move chaotically. The presence of chaos is supported by the results of an estimate of the maximal Lyapunov exponent. It is shown that the streamfunction equation for this flow may be written in the form of a Hamiltonian system and that an expansion of this equation captures all the essential features of the Poincaré sections. Elements of Kolmogorov–Arnol’d–Moser theory, the Poincaré–Birkhoff fixed-point theorem, and associated Hamiltonian dynamics theory are then employed to confirm the existence of chaos in the flow in a rigid alveolated duct.

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