Mathematics and physics are not separated.

At the end of the 19th century, Poincaré et al. put forward the concept of dynamical system in the study of celestial mechanics and the qualitative theory of differential equations.

According to the broadest understanding, the object of study of dynamical systems is the topology and asymptotic behavior of orbits under the action of certain transformation groups, for example, the flow generated by the vector field on the differential manifold is the effect of real number plus groups, and the discrete differential differential dynamical system can be regarded as the effect of integer plus groups.

The modern research on differential dynamical system theory began mainly in the sixties of the 20th century, and countless scholars and teachers went forward to carry out research one after another.

Su Mu has actually been studying differential dynamics a little recently, although the speed of understanding is a little slow because of the complexity of some theories, but after all, he will be greatly improved by cultivating on the basis of his predecessors.

It's just an opportunity.

An inexplicable opportunity.

All the inspiration seemed to converge into a galaxy, and it completely exploded at once, Su Mu even completely forgot the whole world, and devoted himself to this mathematical world, everything in the outside world became small, and there was no way to compete with the mathematical galaxy.

"Methods such as canonical equations and obstacle sets promote the preparation properties and structural stability of differential dynamical systems."

"An obstacle set is a special subset of a finite projective plane, and if the subset K in the projective plane of order q does not contain any line, but intersects every line, then K is called an obstacle set."

"If K is the obstacle set in PG(2,q), then |K|≥1+√q+q。 ”

"The equal sign holds when K is a bell plane. For example, PG(2,q2) can be divided into q2-q+1 Baar subplanes, and if X is the union of t of them, then X is an obstacle set and intersects t points or t+q points with each line. ”

Unconsciously, Su Mu's various ideas were already written all over the scratch paper.

The speed of his words is extremely fast, and there is even a rustling sound, fortunately there are no people passing by, otherwise he would definitely be surprised by his terrifying efficiency, all the efforts during this time have been turned into nutrients, thick and thin.

"The Initial Value of Ordinary Differential Equations, the Existential Uniqueness of the Solution, and the Extension of the Solution."

"Lyapunov's stability in an infinite disturbance in asymptotic stability."

“......”

One sheet.

Two sheets.

Three.

Five sheets.

A total of five pieces of scratch paper were written, some were complicated, some were concise, as long as it was something that Su Mu thought of, he wrote them all!

This state is different from the limit operation used by Su Mu, the limit operation is an overload to increase mental power, but this state is a burst of inspiration!

It's a new experience like never before!

Originally, Su Mu wanted to try whether to use a limit operation superimposed in this state, but he gave up after the thought flashed, because he was afraid that the limit operation would lead to the interruption of the inspiration!

"The beauty of mathematics."

Su Mu's pen has stopped, but his mind is still constantly thinking, thinking of something that is not very reasonable, he will revise and correct it, in the dark, he seems to have penetrated something new, as if he has broken a membrane and opened a new world.

He hopes that the next time he enters this world, it will be smoother and there will be no obstacles.

......

......

"Huh?"

"Wait, I seem to see a friend of mine."

Because it was a weekend, there must be more people in the library than usual, Yue Hao made an appointment with his roommate in the library, and was about to find a place to brush up on the questions to study, but suddenly caught a glimpse of Su Mu's shadow.

After all, they are teammates, and they can talk very well in the Olympiad National Championships and World Championships, Su Mu is still quite recognizable in Yue Hao's eyes, it has been more than a month since the start of school, and he has met Dai Binbin twice in the school cafeteria, but it is the first time he has met Su Mu.

Among the several people in the Olympiad World Championships, Yinhong and Chen Junlang are still in the first and second years of high school, and there are only three graduates of high school, Su Mu and Dai Binbin.

Although he said that all of them came to Peking University, what Yue Hao wanted to complain about very much was that Su Mu finally chose the Department of Physics, and Dai Binbin escorted the Department of Chinese of Peking University, and among the three of them, he was the only one who chose mathematics!!

This incident also made Yue Hao "sad" for a while, and even Chen Bing, the team leader at the time, expressed great regret.

Su Mu had now recovered from that state.

When Yue Hao approached, Su Mu had already discovered him.

When he met his old friend, Su Mu was still very happy, and immediately raised his hand to say hello.

"There's no one in these two locations, right?"

"No one."

Yue Hao was originally going to go upstairs to study, but now he happened to meet Su Mu, smiled, and sat down opposite him.

"This is my roommate, Hu Tu, apprentice's apprentice, don't be confused by his name, he is the highest score in mathematics in our class."

"At that time, he just didn't sign up for the Olympiad, and if he did, he would definitely be able to participate in the World Championship with us." Yue Hao said with a smile, still with the same taste of cross talk: "I'm also a math boss,"

Turning around, Yue Hao also introduced Su Mu to Hu Tu: "Well, this is the Su Mu I told you, he won the special award of this year's Mathematics Olympiad World Championships." ”

Su Mu looked at Yue Hao's roommate, Hu Tu was wearing a small black coat and a pair of black-framed glasses, and he looked very gentle. The style is a bit similar to Lin Shaojun, but obviously much more confident, when Su Mu and him looked at each other, Hu Tu smiled at Su Mu and nodded.

Because it's in the library, you need to keep it quiet, and you can't chat for a long time.

Just lowered his voice and asked casually about the current situation, and sighed a few words that it was really a pity for Su Muxuan to choose physics, Yue Hao and Hu Tu also took out their textbooks and started practicing.

Mathematics has fewer assignments than physics departments.

Now when I first go to university, more of the content is in line with high school mathematics. Of course, at the level of Yue Hao and Hu Tu, they are now already self-studying courses far behind.

"Have you studied differential dynamical systems now?"

Because he had just finished studying this aspect and had made a small breakthrough, Su Mu couldn't help but feel in a good mood and wanted to share his joy with Yue Hao and them.

Although the students in the School of Physics are also good at mathematics, they are definitely not as professional as the students in the Department of Mathematics.

Yue Hao's mathematics is extremely high in Su Mu's evaluation, and now that he has met him, Su Mu subconsciously wants him to help him check the results.

"Differential dynamical systems?" Hearing Su Mu mention this term, and looking at the scratch paper he pushed over, Yue Hao said with some confusion: "That's the content of the extended major course in the third year of mathematics, right?" ”

"I've taught myself a little bit, but I'm not very detailed."

"Then you can help me take a look and see if there is anything wrong, or give advice."

Su Mu's face was overjoyed.

He knew that Yue Hao would not let him down.

Every time Yue Hao said that he couldn't do it, but in fact, he pretended to be a pig and ate a tiger again and again.

"Hmm."

Yue Hao took the opportunity to take over Su Mu's draft paper.

He didn't think that Su Mu would write anything so difficult.

Although he had glimpsed some of Su Mu's scratch paper before, Yue Hao only thought that it might be the calculation process of a certain topic.

After all, Su Mu has now entered the School of Physics.

It may just happen to be interspersed with differential dynamical systems.

"Huh?"

However, after scanning Su Mu's scratch paper.....

"The initial value of an ordinary differential equation, the existential uniqueness of the solution, and the extension of the solution?"

"The continuous dependence and differentiability of the solution on the initial value and the parameters??"

"Lyapunov's stability in asymptotic stability infinitely disturbed?"

“？？？”

Yue Hao's face instantly became a little strange.

.....