In this paper we analyze some dynamical systems, whose motion is not on continuous path, but on a fractal one. Starting from El Naschie's space time and E-Infinity theory we show a mathematical approach based on a potential theory to describe the interaction system-support. We study some relevant force fields on Cantorian space and analyze the differences with respect to the analogous case on continuum. Furthermore, we consider the idea that a Cantorian space could explain some relevant stochastic and quantum processes, if the space acts as a harmonic oscillating support. This means that a quantum process could sometimes be explained as a classical one, but on a non differential and discontinuous support, that is without invoking quantum mechanics. We consider the validity of this point of view, that in principle could be more realistic, because it describes the real nature of matter and space. Indeed, the presently observed large scale structure reflects the phenomenology of the microscopic world. The consequence of this point of view could be extended in many fields such as biomathematics, structural engineering, physics, astronomy, biology and so on.

Dynamical Systems on Cantorian spacetime and applications

IOVANE, Gerardo;SALERNO, Saverio
2005

Abstract

In this paper we analyze some dynamical systems, whose motion is not on continuous path, but on a fractal one. Starting from El Naschie's space time and E-Infinity theory we show a mathematical approach based on a potential theory to describe the interaction system-support. We study some relevant force fields on Cantorian space and analyze the differences with respect to the analogous case on continuum. Furthermore, we consider the idea that a Cantorian space could explain some relevant stochastic and quantum processes, if the space acts as a harmonic oscillating support. This means that a quantum process could sometimes be explained as a classical one, but on a non differential and discontinuous support, that is without invoking quantum mechanics. We consider the validity of this point of view, that in principle could be more realistic, because it describes the real nature of matter and space. Indeed, the presently observed large scale structure reflects the phenomenology of the microscopic world. The consequence of this point of view could be extended in many fields such as biomathematics, structural engineering, physics, astronomy, biology and so on.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4009252
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