{"id":19489961,"url":"https://github.com/cchandre/confkam","last_synced_at":"2026-05-06T00:33:45.342Z","repository":{"id":151252868,"uuid":"364819498","full_name":"cchandre/ConfKAM","owner":"cchandre","description":"Conjugation method in configuration space for invariant tori of Hamiltonian systems","archived":false,"fork":false,"pushed_at":"2022-05-01T07:43:41.000Z","size":60,"stargazers_count":1,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"main","last_synced_at":"2025-01-08T08:42:50.297Z","etag":null,"topics":["conjugation","hamiltonian","hamiltonian-dynamics","invariant-tori","kolmogorov-arnold-moser","numpy","python3","scipy"],"latest_commit_sha":null,"homepage":"","language":"Python","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/cchandre.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2021-05-06T07:17:09.000Z","updated_at":"2023-03-24T16:10:46.000Z","dependencies_parsed_at":"2024-03-14T04:01:25.581Z","dependency_job_id":null,"html_url":"https://github.com/cchandre/ConfKAM","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/cchandre%2FConfKAM","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/cchandre%2FConfKAM/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/cchandre%2FConfKAM/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/cchandre%2FConfKAM/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/cchandre","download_url":"https://codeload.github.com/cchandre/ConfKAM/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":240732048,"owners_count":19848623,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["conjugation","hamiltonian","hamiltonian-dynamics","invariant-tori","kolmogorov-arnold-moser","numpy","python3","scipy"],"created_at":"2024-11-10T21:10:34.660Z","updated_at":"2025-10-29T23:03:06.465Z","avatar_url":"https://github.com/cchandre.png","language":"Python","funding_links":[],"categories":[],"sub_categories":[],"readme":"# KAM in configuration space for invariant tori in Hamiltonian systems\n\n- [`ConfKAM_dict.py`](https://github.com/cchandre/ConfKAM/blob/main/ConfKAM_dict.py): to be edited to change the parameters of the ConfKAM computation (see below for a dictionary of parameters)\n\n- [`ConfKAM.py`](https://github.com/cchandre/ConfKAM/blob/main/ConfKAM.py): contains the ConfKAM classes and main functions defining the ConfKAM map\n\n- [`ConfKAM_modules.py`](https://github.com/cchandre/ConfKAM/blob/main/ConfKAM_modules.py): contains the methods to execute the ConfKAM map\n\nOnce [`ConfKAM_dict.py`](https://github.com/cchandre/ConfKAM/blob/main/ConfKAM_dict.py) has been edited with the relevant parameters, run the file as \n```sh\npython3 ConfKAM.py\n```\n\n___\n##  Parameter dictionary\n\n- *Method*: 'line_norm', 'region'; choice of method                                            \n- *Nxy*: integer; number of points along each line in computations \n- *r*: integer; order of the Sobolev norm used in `compute_line_norm()`                                        \n####                                                                                                   \n- *omega0*: array of *n* floats; frequency vector **\u0026omega;** of the invariant torus                                \n- *Omega*: array of *n* floats; vector **\u0026Omega;** defining the perturbation in actions                             \n- *Dv*: function; derivative of the *n*-d potential along a line                                               \n- *CoordRegion*: array of floats; min and max values of the amplitudes for each mode of the potential (see *Dv*); used in `compute_region()`\n- *IndxLine*: tuple of integers; indices of the modes to be varied in `compute_region()`                                        \n         parallelization in `compute_region()` is done along the *IndxLine*[0] axis   \n- *PolarAngles*: array of two floats; min and max value of the angles in 'polar'\n- *CoordLine*: 1d array of floats; min and max values of the amplitudes of the potential used in `compute_line_norm()`   \n- *ModesLine*: tuple of 0 and 1; specify which modes are being varied (1 for a varied mode)     \n- *DirLine*: 1d array of floats; direction of the one-parameter family used in `compute_line_norm()`                 \n####                                                                                           \n                                         \n####                                                                                                           \n- *AdaptSize*: boolean; if True, changes the dimension of arrays depending on the tail of the FFT of *h*(*\u0026psi;*)      \n- *Lmin*: integer; minimum and default value of the dimension of arrays for *h*(*\u0026psi;*)                           \n- *Lmax*: integer; maximum value of the dimension of arrays for *h*(*\u0026psi;*) if *AdaptSize* is True                   \n####                                                                                                         \n- *TolMax*: float; value of norm for divergence                                                      \n- *TolMin*: float; value of norm for convergence                                                           \n- *Threshold*: float; threshold value for truncating Fourier series of *h*(*\u0026psi;*)                                   \n- *MaxIter*: integer; maximum number of iterations for the Newton method                                      \n####                                                                                                         \n- *Type*: 'cartesian', 'polar'; type of computation for 2d plots                                             \n- *ChoiceInitial*: 'fixed', 'continuation'; method for the initial conditions of the Newton method   \n- *MethodInitial*: 'zero', 'one_step'; method to generate the initial conditions for the Newton iteration          \n####                                                                                                       \n- *AdaptEps*: boolean; if True adapt the increment of eps in `compute_line_norm()`                                   \n- *MinEps*: float; minimum value of the increment of eps if *AdaptEps*=True                               \n- *MonitorGrad*: boolean; if True, monitors the gradient of *h*(*\u0026psi;*)                                      \n####                                                                                 \n- *Precision*: 32, 64 or 128; precision of calculations (default=64)                  \n- *SaveData*: boolean; if True, the results are saved in a `.mat` file               \n- *PlotResults*: boolean; if True, the results are plotted right after the computation              \n- *Parallelization*: tuple (boolean, int); True for parallelization, int is the number of cores to be used (set int='all' for all of the cores)\n####\n---\nReference: A.P Bustamante, C. Chandre, *Numerical computation of critical surfaces for the breakup of invariant tori in Hamiltonian systems*, [arXiv:2109.12235](https://arxiv.org/abs/2109.12235)\n```bibtex\n@misc{bustamante2021,\n      title = {Numerical computation of critical surfaces for the breakup of invariant tori in Hamiltonian systems}, \n      author = {Adrian P. Bustamante and Cristel Chandre},\n      year = {2021},\n      eprint = {2109.12235},\n      archivePrefix = {arXiv},\n      primaryClass = {math.DS}\n}\n```\n\nFor more information: \u003ccristel.chandre@cnrs.fr\u003e\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fcchandre%2Fconfkam","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fcchandre%2Fconfkam","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fcchandre%2Fconfkam/lists"}