Domains of analyticity and Lindstedt expansions of KAM tori in some dissipative perturbations of Hamiltonian systems

Nonlinearity ◽  
2017 ◽  
Vol 30 (8) ◽  
pp. 3151-3202 ◽  
Author(s):  
Renato C Calleja ◽  
Alessandra Celletti ◽  
Rafael de la Llave
Keyword(s):  
Hamiltonian Systems ◽  
Kam Tori

Geometric Averaging of Hamiltonian Systems: Periodic Solutions, Stability, and KAM Tori

2011 ◽  
Vol 10 (3) ◽  
pp. 817-856 ◽  
Author(s):  
Kenneth R. Meyer ◽  
Jesús F. Palacián ◽  
Patricia Yanguas
Keyword(s):  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Kam Tori

scholarly journals Geometry of KAM tori for nearly integrable Hamiltonian systems

2007 ◽  
Vol 27 (03) ◽  
pp. 725 ◽  
Author(s):  
HENK BROER ◽  
RICHARD CUSHMAN ◽  
FRANCESCO FASSÒ ◽  
FLORIS TAKENS
Keyword(s):  
Hamiltonian Systems ◽  
Kam Tori ◽  
Integrable Hamiltonian Systems ◽  
Nearly Integrable Hamiltonian Systems

Deterministic Mechanism of Irreversibility

2018 ◽  
Vol 14 (3) ◽  
pp. 5708-5733 ◽  
Author(s):  
Vyacheslav Michailovich Somsikov
Keyword(s):  
Internal Energy ◽  
Hamiltonian Systems ◽  
Classical Mechanics ◽  
Motion Equation ◽  
Holonomic Constraints ◽  
Dissipative Processes ◽  
Motion Energy ◽  
Analytical Review ◽  
History Of ◽  
Material Points

The analytical review of the papers devoted to the deterministic mechanism of irreversibility (DMI) is presented. The history of solving of the irreversibility problem is briefly described. It is shown, how the DMI was found basing on the motion equation for a structured body. The structured body was given by a set of potentially interacting material points. The taking into account of the body’s structure led to the possibility of describing dissipative processes. This possibility caused by the transformation of the body’s motion energy into internal energy. It is shown, that the condition of holonomic constraints, which used for obtaining of the canonical formalisms of classical mechanics, is excluding the DMI in Hamiltonian systems. The concepts of D-entropy and evolutionary non-linearity are discussed. The connection between thermodynamics and the laws of classical mechanics is shown. Extended forms of the Lagrange, Hamilton, Liouville, and Schrödinger equations, which describe dissipative processes, are presented.

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