Nekhoroshev and Kam Stabilities in Generalized Hamiltonian Systems
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We present some Nekhoroshev stability results for nearly integrable, generalized Hamiltonian systems which can be odd dimensional and admit a distinct number of action and angle variables. Using a simultaneous approximation technique due to Lochak, Nekhoroshev stabilities are shown for various cases of quasi-convex generalized Hamiltonian systems along with concrete estimates on stability exponents. Discussions on KAM metric stability of generalized Hamiltonian systems are also made.