We are here with the Part 4 of the Arithmetical Dynamics Series. Let's get started.... Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. $P^{m}(z)=z$ and $P^{N}(z)=z$ where $m\left|N \Rightarrow\left(P^{m}(z)-z\right)\right|\left(P^{N}(z)-z\right)$ The proof of the theorem in Part 0 : Let , P be the polynomials satisfying the hypothesis of theorem 6.2.1 […]
We are here with the Part 3 of the Arithmetical Dynamics Series. Let's get started.... Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. Theory: Let \( \{ \zeta_1 , ......., \zeta_m \} \) be a ratinally indifferent cycle for R and let the multiplier of \( R^m \) at each […]
We are here with the Part 2 of the Arithmetical Dynamics Series. Let's get started.... Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. The lower bound calculation is easy . But for the upper bound , observe that each \( z \in K \) lies in some cycle of length […]
We are here with the Part 1 of the Arithmetical Dynamics Series. Let's get started.... Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. Definition: Suppose that \( \zeta \in C \) is a fixed point of an analytic function \( f \) . Then \( \zeta \) is : a) […]
Invariance is a fundamental phenomenon in mathematics. In this combinatorics problem from ISI Entrance, we discuss how to use invariance.
This beautiful application from SMO(senior)-2014 is based on the concepts of Number Theory . Sequential hints are provided to understand and solve the problem .
This beautiful application from SMO(senior)-2014/Problem 4 is based Number Theory . Sequential hints are provided to understand and solve the problem .
Fibonacci Number matrix is closely related with fibonacci numbers (no wonder)! They have curious power to create curves on a torus. Welcome to the adventure