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Exponentially small splitting of separatrices for area-preserving maps
Affiliation:1. School of Psychiatry, University of New South Wales, Sydney, NSW, Australia;2. Early Psychosis Programme, The Bondi Centre, South Eastern Sydney Local Health District, Australia;3. Musculoskeletal Division, The George Institute for Global Health and School of Public Health, The University of Sydney, Sydney, New South Wales, Australia;4. UPC KU Leuven, Campus Kortenberg, KU Leuven – University of Leuven, Department of Neurosciences, Kortenberg, Belgium;5. KU Leuven–University of Leuven, Department of Rehabilitation Sciences, Leuven, Belgium;6. St John of God Health Care Richmond Hospital North Richmond, Australia;7. Clinical Research Unit for Anxiety and Depression, School of Psychiatry, University of New South Wales at St Vincent''s Hospital, Darlinghurst, NSW, Australia;8. Schizophrenia Research Unit, South Western Sydney Local Health District, Australia;9. Physiotherapy Department, South London and Maudsley NHS FoundationTrust, Denmark Hill, London SE5 8AZ, United Kingdom;10. Health Service and Population Research Department, Institute of Psychiatry, King''s College London, De Crespigny Park, London SE5 8 AF, United Kingdom;1. Department of Economics, Cornell University, 404 Uris Hall, Ithaca, NY 14853, USA;2. Department of Statistics & Data Science, Cornell University, 1170 Comstock Hall Cornell University, Ithaca, NY 14853, USA;3. School of Operations Research and Information Engineering, Cornell University, 238 Rhodes Hall Cornell University Ithaca, NY 14853, USA;1. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P. O. Box 80207, Jeddah, 21589, Saudi Arabia;2. Department of Mathematics, Quaid-I-Azam University, 45320, Islamabad, 44000, Pakistan;1. Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan;2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P. O. Box 80207, Jeddah 21589, Saudi Arabia;1. Departamento de Matemática Aplicada and IUMA, University of Zaragoza, E-50009 Zaragoza, Spain;2. Computational Dynamics group, University of Zaragoza, E-50009 Zaragoza, Spain;3. Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland
Abstract:We discuss some recent lower and upper bounds for the splitting of separatrices for close-to-identity area-preserving maps.
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