Adiabatic invariant of the harmonic oscillator, complex matching and resurgence

Keywords

Mathematics, Harmonic oscillator, Singularity, Riccati equation, Mathematical analysis

References

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• Classification analytique des 'equations di 'erentielles non lin'eaires r'esonantes du premier ordreJean Martinet, Jean-Pierre Ramis — 1983
• Résurgence paramétrique et exponentielle petitesse de l'écart des séparatrices du pendule rapidement forcéDavid Sauzin — 1995
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• Exponential AsymptoticsR. E. Meyer — 1980
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Cited by

• Pair Production in a Uniform Electric FieldJaume de Haro — 2003
• Resurgence in a Hamilton-Jacobi equationC. Olivé, David Sauzin, Tere M. Seara — 2003
• Borel summation and splitting of separatrices for the Hénon mapVassili Gelfreich, David Sauzin — 2001
• An introduction to resurgence, trans-series and alien calculusDaniele Dorigoni — 2014
• Resumació de Borel i teoria de la ressurgènciaM. Teresa Martínez-Seara, David Sauzin — 2003
• Lectures on non‐perturbative effects in large N gauge theories, matrix models and stringsMarcos Mariño — 2012
• Universality and asymptotics of graph counting problems in non-orientable surfacesStavros Garoufalidis, Marcos Mariño — 2008
• The inner equation for one and a half degrees of freedom rapidly forced Hamiltonian systemsInmaculada Baldomá — 2006
• Exponentially small splitting of separatrices beyond Melnikov analysis: rigorous resultsInmaculada Baldomá, Ernest Fontich, Marcel Guàrdia — 2012
• Exponentially Small Splitting for the Pendulum: A Classical Problem RevisitedMarcel Guàrdia, C. Olivé, Tere M. Seara — 2010
• On Exponentially Small Effects in Dynamical Systems with a Small ParameterOleg Zubelevich — 2005
• Lectures on non-perturbative eects in large N gauge theories, matrix models and stringsMarcos Mari — 2014
• Resurgence in topological string theoryRicardo Couso-Santamaría — 2014
• Thèse d'habilitation à diriger des recherches en mathématiques. Contribution à la théorie des perturbations des systèmes hamiltoniens et à la théorie de la résurgence.David Sauzin — 2004
• Intrinsic Dissipation Due to Mode Coupling in Two-Dimensional-Material Resonators Revealed Through a Multiscale ApproachSubhadeep De, Arend M. van der Zande, N. R. Aluru — 2020
• Resurgence and 1/N Expansion in Integrable Field TheoriesLorenzo Di Pietro, Marcos Mariño, Giacomo Sberveglieri — 2021
• On the Structure of Trans-Series in Quantum Field TheoryMarcos Mariño, Ramon Miravitllas, Tomás Reis — 2023
• Advanced Asymptotic MethodsC. Kuehn — 2015
• D ec 2 00 8 UNIVERSALITY AND ASYMPTOTICS OF GRAPH COUNTING PROBLEMS IN UNORIENTED SURFACESS. Garoufalidis, Marco Marino — 2009
• Resurgence in a Hamilton-Jacobi EquationCC. Olivé, D. Sauzin, T. M. Seara — 2002

Related papers

• Numerical study of a many-particle adiabatic invariantPoul G. Hjorth, T. M. O’Neil — 1987
• Non-adiabatic changes in the second invariant JR. J. Hastie, J. B. Taylor — 1982
• Perturbation to symmetries and adiabatic invariant for systems of generalized c lassical mechanicsYi Zhang, Mei Feng-Xiang, (1)北京理工大学应用力学系，北京 100081; (2)苏州科技学院土木工程系，苏州 215011 — 2003
• Adiabatic invariant and evaluation of particle loss in helical torusJiro Todoroki — 1990
• Geometric factors in the adiabatic evolution of classical systemsFernando Casas, J A Oteo, J.M. Gómez-Ros — 1992
• Orbits in Adiabatically Contracting Spherical PotentialsR. Jesseit, Andreas Burkert — 2003
• Guiding Center Motion and Plasma Behavior in the Bumpy TorusG. Gibson, W. C. Jordan, E.J. Lauer — 1964
• Area Spectrum of a Kerr-Newman Black Hole Via an Adiabatic InvariantXiao-Xiong Zeng, Q. Li — 2014
• Changes in adiabatic invariantsJoseph B. Keller, Ye Mu — 1991